I think you could use this informally, with friends/as a 'home sign'. Or if you were doing a speech/presentation where you would be repeating the word a lot you could fingerspell it once and signal that you are going to use that sign for platinum. For any new people you meet though they probably wouldn't immediately guess what you meant if you used 'P' the same as gold/silver, so then you may have to switch to fingerspelling, just for clarity. I think in most casual/informal situations and especially with friends it can be helpful to develop signs for a word you might use often, or that is hard to spell Just an opinion/my thoughts from my experience though, not a rule for signing in general.
The sign for Wales is to hold up your three middle fingers bent slightly forward (like a claw), and move your hand straight downwards.
The sign for Rose is the same as 'flower' but you use the lip-pattern (mouthing the word) rose, the sign is put your finger and thumb together and touch either side under your nose, like smelling a flower.
The sign for diamond is your non-dominant hand held flat, palm down (As if you were going to show someone your ring) and your dominant hand on top of that hand, fingers together and then open and close them quickly, as if to show sparkling of a diamond.
There isn't an actual sign for platinum you would fingerspell p-l-a-t-i-n-u-m. You could use the sign for metal with the lip-pattern platinum, the sign for metal is your index finger taps your chin twice.
Video (for metal) here:
Hope this helps
I don't think there is one, you would finger spell c-y-a-n, you could use the sign for blue, that would be the closest actual sign. You could combine fingerspelling followed by the sign for blue straight after, that would probably be the clearest way to sign it with an actual sign.