Don't worry bro. Worst case scenario, you'll probably have to get the meter removed, plastic disassembled (it's usually clipped on to the meter), detailed and installed back again. If this happens the meter might display some errors upon reinstallation which may need to be removed.
Saying this is 'worst case' because you definitely won't need to replace the entire instrument cluster. BTW, I've used both polishes and compounds on meters of some old cars that I've kept - and have not had any adverse consequences.