If F, then, depending on mechanical duty, a stabilised austenitic like 321 or 347 springs to mind. it's non-magnetic as long as it's not cold worked. (Note that this temperature will sensitize an unstabilized grade. Depending on your environment, it might well then corrode.) However, it's not a brilliant electrical conductor. Depends how good a conductor you need it to be.
If temp is C, you're into some relatively exotic stuff beyond my ken.