According to Appendix E, "PRONUNCIATION OF WORDS AND NAMES", the pronunciation of the initial sound of "when" might be different from the "w" sound in words like "winter" and "will". It says "W has the sound of English w. HW is a voiceless w, as in English white (in northern pronunciation). Wikipedia's article on The Pronunciation of English "wh" says that this voiceless variant of wh is still common in Scotland and Ireland. Perhaps this is what the appendix means by "northern pronunciation". I spent a bit of time listening to recordings of Tolkien reading and could not hear the distinction, but my ear is not very good. But as someone who has been a member of Baroque choir for years, the distinction is often more important in singing or formal speaking than in casual speaking. And Bilbo is singing, not casually speaking. So perhaps it's not five "w" sounds in a row, but four "w" sounds with "wh" in the middle.