The stations I rent from typically have just the key, remote, and the tag. I know some put all the keys and remotes with the tags, which I can imagine being very bulky.

Either way, I think it would not be wise to cut the chain unless 1) you can put it back exactly as you got it before you returned it; 2) you're absolutely sure you won't misplace the items if separated (or are willing to pay the lost key fee if accused of losing one of the items).