Thanks, Joojaa.
I did some testing and did ultimately discover that changing the UVs doesn't affect the weights in my case. I am working on skinning a hand so I had a perfect replication on the other side to test Mirror Skin Weights. The other hand has a totally different mapped UV but the Mirror Skin Weights has worked (so far so good). This, to me, indicates it's not reliant on the UVs.
However, in the help file it claims that Copy Skin Weights and Export Skin Weights does indeed use UVs.
Moral of the story: If you need to Paint Skin Weights on one of two identical or mirrored objects then follow this sequence for best results. I'm proof that it can be done another way, but it's not ideal.
- Make your first model.
- Map the UVs.
- Duplicate the model.
- Paint Skin Weights.
- Copy/Mirror/Exp-Imp Skin Weights to duplicated model.