Aluminum can be soldered quite easily, it just takes the right solder (and that might be a bit hard to get for a hobbyist).
It can also be glued reliably with eg. supper glue or epoxy - as long as the areas to be bonded is CLEAN (the oxide doesn't prevent gluing).
It can be welded as well.
That said, I'd like to second the poster suggesting pop-rivets (or just use plain old rivets), if screws are a no-no. Personally I'd go with the kind of self tapping screws made for thin plate - they don't have to be much longer thanthe material to be joined.