Though I'm not sure what chinchilla proofing entails, hedgehogs are much smaller and can squeeze into tight places. You will need to take the time to go over the room inch by inch to make sure everything is tucked away and there are no hiding spots or danger areas. They also like to annoint over everything and anything so a few tips:
-no chemical floor washing or carpet cleaners
-no where they can fall or squeeze into. I fill socks with beans or rice, sew them shut, cover them with another sock (so that I can eaasily remove it and wash it when it gets dusty). I use the socks everywhere to plug up holes, block under the couch etc.
-I use play pen pieces (or C&C cubes) to block to hedgehog into one safe room (easier to control one area than the whole house
-no wires or dangerous items they can get into
-watch them at all times obviously and make sure everyone knows they are there (as they are smaller, the potential exists for someone to forget what is underfoot)
-I let them out on a hardwood floor and no where near the carpet (some carpets are easy for them to get stuck on with their nails, also some hedgies like to be...messy...)
-I give them PVC tubes to run through (and also to seek shelter in case they become frightened)
Not all hedgies like to free run in a room. It is a big open area for a small animal. My blind hedgies however have loved it and would do laps for hours.