My point is to not create such methods. Instead create a corresponding method on the index type. If you like, you're pretending that the SquareIndex is the Square. It may be a little unfamiliar at first, and could involve extraneous lookups, but ultimately you're just treating your index as if it were a reference, which works fine. It helps to use the newtype pattern to create strongly typed indexes.
I'll also note that as I usually think of it, an arena is just a Vec, which works great as long as object deletion isn't important either because they aren't deleted or because they're small or because not too many are allocated.