Yeah, you could put some paper towel down next time inside your tank (just make sure your rodent is completely dry also, and nothing will stick to it..) I dont think you need to feed in a seperate container, that just stresses them out.
Imo your snake will be fine. Its not like they dont get some "substrate" in their mouth in the wild.
BUT!, they may get tank aggressive . that wouldnt be good,
Reptiles
0.0.1 - Rhacodactylus Ciliatus, Cheerio
Mammals
1.1 - Canis Lupus Familiaris, Little Man & Molly