Certainly, I can share your dwarf art for the final Silm Film session of Season 4, Kathrin. If I recall correctly, the final word on beards on dwarf women was that we could give it a try, and if we could come up with artwork that wasn't ridiculous, they'd go for it. Basically, it was a 'go ahead and convince us' decision. Hopefully, seeing your images will invite them to comment further on how they imagine dwarf men and women distinguishing themselves from one another visually.
And I think this is a relevant Season 4 question with the presence of Dís in the Frame and Telchar in the main story. I would say that, as written, Dís is more clearly a female character. Telchar's main trait is her craftsmanship, and she is not defined by her relationships. She is, presumably, unmarried and without children. Whereas Dís is clearly mourning the deaths of her brother and her sons, and that alone makes the audience identify her as a woman moreso than they would with Telchar. So, I think there would be a stronger impulse to picture Dís in a dress with braids, etc.
I know I've shared this image before, but here's my friend Sasha, costuming as Tinkerbell and Thorin Oakenshield:
Obviously, a lot of work goes into the transformation to Thorin - there is a bodysuit under the armor to alter musculature, and a wig and beard and eyebrows and ears, and about 2 hours worth of putting on makeup. Whereas Tink is wig, ears and makeup (which likely takes significantly less time, but I haven't seen her get into Tinkerbell, so I wouldn't know for sure). Sasha is clearly a skilled chameleon, who can transform her appearance at will, but worth pointing out that this is something done for fun and not professionally - so certainly, a costume and makeup crew on a TV show can easily achieve similarly impressive results with altering a person's appearance in terms of age or gender or apparent height/build, etc.
Saying that outsiders can't tell the difference is not the same thing as saying that there is no difference. I would not be surprised to learn that some white people have trouble telling the difference between male and female Asians (and not just people intentionally being ambiguous with the Visual Kei stuff)*. Cheekbones tend to give away feminine facial features, but that can be disguised with contouring, so it's certainly possible to use makeup to give a more masculine or feminine look to anyone's face. But it's also true that cheekbones are going to be a bit different in Caucasian and Asian faces, so if you've trained your eye to identify 'male' and 'female' by looking at the face and unconsciously looking at how high the cheekbones are, that tell won't read the same and the brain can get confused.
Elf designs are often quite androgynous, right? So if someone commented that outsiders couldn't tell male and female elves apart, we'd just say that it means that the women aren't very busty and are maybe taller than you'd expect, and the guys are all clean shaven and have long hair, with everyone having a build leaning towards 'slender'. Put like that, you could understand the confusion. So, we could have a similar level of similarity/confusion between male and female dwarves as seen by outsiders - maybe the women have deeper voices than you expect, and you can't exactly check for an Adam's apple under the beard. Etc.
Basically, if Elves and Dwarves have slightly different secondary sexual characteristics, they would be easily confused by one another...but that doesn't mean there is no actual difference between the appearance of men and women in either group. And certainly, with Men trained to recognize the dichotomy between male and female humans, they're likely to think the beardless elves are all much younger than they actually are, and the bearded dwarves more universally male than they actually are.
* There was an entire episode of Bones where one of the questions was whether a character was male or female. Like, the office gossip was on people trying to figure out the gender of an androgynous-presenting Japanese person. Don't ask me why the writers thought this a good plan, but there you go.
And I think this is a relevant Season 4 question with the presence of Dís in the Frame and Telchar in the main story. I would say that, as written, Dís is more clearly a female character. Telchar's main trait is her craftsmanship, and she is not defined by her relationships. She is, presumably, unmarried and without children. Whereas Dís is clearly mourning the deaths of her brother and her sons, and that alone makes the audience identify her as a woman moreso than they would with Telchar. So, I think there would be a stronger impulse to picture Dís in a dress with braids, etc.
I know I've shared this image before, but here's my friend Sasha, costuming as Tinkerbell and Thorin Oakenshield:

Obviously, a lot of work goes into the transformation to Thorin - there is a bodysuit under the armor to alter musculature, and a wig and beard and eyebrows and ears, and about 2 hours worth of putting on makeup. Whereas Tink is wig, ears and makeup (which likely takes significantly less time, but I haven't seen her get into Tinkerbell, so I wouldn't know for sure). Sasha is clearly a skilled chameleon, who can transform her appearance at will, but worth pointing out that this is something done for fun and not professionally - so certainly, a costume and makeup crew on a TV show can easily achieve similarly impressive results with altering a person's appearance in terms of age or gender or apparent height/build, etc.
Saying that outsiders can't tell the difference is not the same thing as saying that there is no difference. I would not be surprised to learn that some white people have trouble telling the difference between male and female Asians (and not just people intentionally being ambiguous with the Visual Kei stuff)*. Cheekbones tend to give away feminine facial features, but that can be disguised with contouring, so it's certainly possible to use makeup to give a more masculine or feminine look to anyone's face. But it's also true that cheekbones are going to be a bit different in Caucasian and Asian faces, so if you've trained your eye to identify 'male' and 'female' by looking at the face and unconsciously looking at how high the cheekbones are, that tell won't read the same and the brain can get confused.
Elf designs are often quite androgynous, right? So if someone commented that outsiders couldn't tell male and female elves apart, we'd just say that it means that the women aren't very busty and are maybe taller than you'd expect, and the guys are all clean shaven and have long hair, with everyone having a build leaning towards 'slender'. Put like that, you could understand the confusion. So, we could have a similar level of similarity/confusion between male and female dwarves as seen by outsiders - maybe the women have deeper voices than you expect, and you can't exactly check for an Adam's apple under the beard. Etc.
Basically, if Elves and Dwarves have slightly different secondary sexual characteristics, they would be easily confused by one another...but that doesn't mean there is no actual difference between the appearance of men and women in either group. And certainly, with Men trained to recognize the dichotomy between male and female humans, they're likely to think the beardless elves are all much younger than they actually are, and the bearded dwarves more universally male than they actually are.
* There was an entire episode of Bones where one of the questions was whether a character was male or female. Like, the office gossip was on people trying to figure out the gender of an androgynous-presenting Japanese person. Don't ask me why the writers thought this a good plan, but there you go.