Let me tell about my grandma:
She sweared to know the best way for cleansing up our table silver - using some common tooth paste and a soft flannel cloth to polish it with smooth circular motions. - I’ve seen it with my own eyes: It really works with silver to get it bright and shiny.
Some of its patina remains in the deep of relief what improves appearance of surface ornaments. The only thing: Silver is a hard metal against aluminium is very soft…( cleanipedia: What Products Can I Use When Cleaning Silver?)
So what, we use the paste to clean, whiten and polish our teeth – and to avoid acidic reactions, what may harm its enamel.
Though, if I had the problem with an old aluminium shell to clean, I would try that method of my grandma first and - of course – beginning somewhere on a little spot at the edge of the lower part of the body. You can see then, whether it works, what happens with metal surface and how do you like the finish – and if “yes”, go so on. - And you may proof several products and take your best choice.
Use tooth paste without additional water – as dry as possible - that prevents ingress of water into said micro cracks. The cloth you need should be very soft: I’d do it with chamois leather. For heavily soiled spots I’d try it very gently with a Scotch Brite or at least with some of that kind of cotton cloth used for body peeling in Hamam …Remark:
All these tips are not approved, so you shall do it on your own risk.