I've been pondering this myself. We had to have one of my cats (the one in my profile pic) put down last month, and we got a fur clipping, as well as her ashes. I'd like a piece of memorial jewelry or glass and I'm finding I'm OK with stuff that includes the fur, but not OK with cremation jewelry/cremation glass, and I don't really know how to articulate why. I think part of it is that fur and hair are shed throughout a lifetime anyway, but dividing up someone's bones or ashes almost feels like commodification to me.
(To be clear: I'm not judging other people who do this with their loved ones' remains, be they human or animal; this is just, like, my opinion, man.)
Also: you might like Caitlin Doughty/Ask A Mortician's videos and/or books. A lot of discussion about different cultures' approaches to death and how people's attitudes have evolved over time.