I like the impulse to have Celegorm and Curufin send Aredhel off to Gondolin with a physical memento that the audience can see her wearing later. And obviously, white fur would fit Aredhel's costume needs well enough. Especially if it's basically a shoulder wrap with a cape sewn to it.
I have qualms about using the pelt of a sentient creature. That is like the giants in Narnia hunting and eating the Talking Stag (and, surprise surprise, they have no qualms about eating humans, either). I can see orcs dressing themselves up in the body parts of their enemies, but I have trouble seeing elves doing that. Even brutal Fëanorean elves. It's a level of barbarism that goes beyond 'hunting' or 'battle' to display trophies like scalps, shrunken heads, dried ears, skulls, etc., and then to turn these into ornament/decoration/wear them. By having the characters refer to their enemy by name, they are clearly aware that what they are fighting is not a beast, but a creature with intelligence and the ability to speak. Sure, they are evil and they are the enemy, and as servants of Morgoth they can be killed with impunity. But skinned for cloaks? I am brought up short there.
Beorn does tack up a warg pelt in The Hobbit. I realize that Beorn only loosely fits into the greater context of Middle-earth, but part of the whole point of his character is that he is part beast. I don't really see the princes of the Noldor making similar choices. But also important to note that, in that case, the body did not vanish but remained to be skinned. Still, the vanishing werewolf bodies from Caradhras in Lord of the Rings do pose a challenge. When we discussed these creatures in Silm Film, we decided that there were several types: embodied Maiar spirits, such as Tevildo and Thuringwethil. Were-creatures, that Sauron had forced spirits into, as Draugluin. And then finally...beasts that are in the employ of the enemy. These are not imbued with any particular spirit or intelligence, but are just wolves, bats, etc. These last definitely leave bodies behind. I'd have to go relisten to that podcast to make sure I remembered all the details correctly.