My friend was in a similar situation some years ago when his much-loved twin pet monkeys contracted some sort of virus and died suddenly.
He took them to the local taxidermist, who told him it would be no problem at all to stuff them. The taxidermist said 'would you like them mounted'?
My friend said 'No, no, just holding hands will be fine'.
Incidentally, some years ago the father of one of my trainee reporters was a member of a group of amateur taxidermists in South Wales. Because professional taxidermy is no longer a common craft in the UK (unlike in France...) they were contracted to stuff a young giraffe and he had to remove part of his garage roof so the job could be done. This is absolutely true.