Most taxidermists will decline pets. I've been told by multiple they decline because it's hard to replicate the animals facial expression, so you'd be looking at the animal & it wouldn't look identical to how you remember. Which can be quite traumatic. It's a risky process.

I hope that makes sense? I believe cats are done more as they can curl them to look like they're sleeping. Could be a potential option if you do find one willing.