A) Imagine the following: It is Shabbat, and I am using spring-loaded hair clips or bobby pins to attach a kippah to my hair. The clips or pins are NOT sewn to the kippah: instead, they are discrete and separate. I don't live inside an eruv. May I walk from a private domain to a public domain on Shabbat? Or would this count as transferring between domains?
B) What if the clips or pins are clipped or pinned to the kippah, but not to my hair? (In this situation, instead of holding the yarmulke on my head, the clips really are doing nothing at all.)
Please cite sources.