When you say aluminum wrap, do you mean aluminum foil? Aluminum foil is only unsafe when it's the kind that has a nonstick layer-- if I'm not mistaken I think Reynold's makes a certain aluminum foil with a nonstick something or another. Otherwise, plain aluminum foil is totally safe, as are aluminum baking sheets. You just have to be careful because sometimes when you scrub them very hard, flakes can come off because aluminum is very soft.
I've ordered from Mighty Nest-- not for bird things, but general housewares-- and had a good experience.