it does seem to be good to make sure the mouse is dry as well as warm. After I wamred mine up in the water, I dried it off really well and fluffed it up.
Also, my mouse came in a bag where his head was bent/tucked under really hard, so Uli had some problems with it (tried swallowing it backwards without much success...hehe) so the next time I made sure it's neck was all straight and it looked pretty much like a "real" mouse.
Also, if your snake had been eating live and you plan to feed in his normal enclosure, it might be good to put some newspaper over the substrate. Like I said, Uli had issues the first time- she wasn't even sure it was food at first- and she got it covered in Aspen while she was trying to swallow it.