I use the same files, sandpaper, rubber wheels, etc. on silver, gold, and platinum without any problems.
The potential for cross contamination is only a real problem with it comes to working with platinum when it is hot. When the metal is cool, any dust, dirt, filings, etc aren’t going to magically incorporate themselves into the metal/alloy. Metals are only going to combine under high temperatures (what temp depends on the metal). If you’re cleaning your pieces before soldering and your solder is clean/uncontaminated then you shouldn’t have any problems with any metals.
A full ‘platinum only’ set of tools is not needed, don’t waste your money; only buy platinum specific tools for working with platinum when it is hot. Platinum fuses to itself, no solder needed, so there is no need for a separate soldering pick though if you want one, they’re cheap. If you’re using a third hand, then the jaws need to be tungsten and not tool steel. You can’t use any binding wires; they can’t take the heat required to work platinum and will contaminate the piece. If you’re melting platinum, a platinum only crucible (of appropriate material) is needed.