Do I have to pay the ticket first, to appeal?
No, you don't have to pay to appeal. Note, appeals are done by mail not online.
But I don't think you have a basis to appeal based on the color. The first ticket is a different violation, the judge did not write what was defective, it can be for multiple reasons which I have done in the past, including not specifying which plate or even that NY can't enforce a plate regulation on an out of state vehicle like necessitating 2 plates.
You can share the ticket number and can possibly find other defects