If you want to divide a tank (or critter keeper?), you'll have to clean a lot more often. You may have issues with trying to evenly distribute heat, which a filter would help with - but in a small space, a filter may end up stressing out both the fish.
I'm not even sure of the dimensions of the critter keeper, but looking at my 2.5 gallon tank... I *could* see both having space, but I can also imagine the amount of ammonia build up
I don't feel like doing a crap-ton (literally) of cleans!!
I have had some Bettas nom on little pond snails. Then spit them out... And the silly snail would STILL be alive. Don't say no to nerites too quick! From the sounds of it, they are a lot bigger than what can fit in his mouth.
BUT... Always depends on how aggressive he is. I have had snails murdered (APPLE snails...) by some, others gone missing, and some Bettas were strictly alone due to their fierce attitudes. Others had zero issues with fish, frogs, or snails.