Firstly, I suspect that oxidation will throw a spanner into any such plan. For metals like aluminum, which have a very high affinity for oxygen, a "virgin" surface will begin to tarnish almost immediately.
The second problem is that metals have microstructure. Neighboring crystals in a polycrystalline aggregate such as a metal piece have to satisfy certain restrictions, you can't put them back willy-nilly. So cold welding never gives you back the exact same structure, there must be some changes locally.
If, however, you can prevent the surfaces from tarnishing and press the surfaces of the broken pieces together - it will cause plastic flow locally and cause the pieces to `weld'.