Vermin corpses not rotting is extremely annoying because there are so many of them.
To fix for now, delete [SMALL_REMAINS] from all vermin in raw files (located in xxx\df\raw\objects). Relevant files, APPROXIMATELY from most annoying vermin to least, depending on biome:
creature_insects.txt
creature_amphibians.txt
creature_small_mammals.txt
creature_reptiles.txt
creature_subterranean.txt
creature_standard.txt
creature_annelids.txt
creature_birds.txt
creature_small_ocean.txt
creature_small_riverlake.txt
Notepad++ is extremely useful here since it will allow you to simply open every file and mass replace [SMALL_REMAINS] with a blank line, or simply SMALL_REMAINS with no brackets so that you can fix it easily if you'd like. Always back up your original raws before modding, of course.
You will probably have to re-generate your world for this to take effect, or your world might not even work at all.
This will prevent you from using vermin corpses for anything, if there are any uses for them (I thought I saw something about extracts from dead vermin now, but I'm not sure), because vermin will not leave corpses any longer. It might also prevent starving dwarves from eating vermin, though I believe they will eat them raw.
You will still need cats to kill vermin. There just won't be any remains left afterwards, until Toady fixes the problem.