Anti-perspirants do not contain aluminum, they contain aluminium oxide. This is the active ingredient which effectively shuts down the sweat glands and so it is not possible to buy an alternative (some contain zirconium oxide instead but the idea is the same). However, sweating is a natural process used to cool the body down so why would you want to stop that? If you don't sweat under your arms you will sweat somwhere else. A final thought, if you are worried about aluminium or aluminium oxide I presume that you do not use any of the following:- aluminium pans, aluminium (cooking) foil, aluminium drinks cans and aluminium aersol cans.
There is an interesting link at
http://www.reverseaging.net/anti-perspirant/