Bronze probably will (it is often alloyed with nickel). Titanium is usually not alloyed with nickel (except as nitinol, a shape-memory alloy used in things like orthodontic braces and vascular stents) so it should be okay. Platinum is also not usually alloyed with nickel except for research and technological applications (i.e. not watches, which are considered jewelry; jewelry-grade platinum is not alloyed with nickel), so you should be okay with platinum cases/bracelets on watches as well.
Bronze probably will (it is often alloyed with nickel). Titanium is usually not alloyed with nickel (except as nitinol, a shape-memory alloy used in things like orthodontic braces and vascular stents) so it should be okay. Platinum is also not usually alloyed with nickel except for research and technological applications (i.e. not watches, which are considered jewelry; jewelry-grade platinum is not alloyed with nickel), so you should be okay with platinum cases/bracelets on watches as well.