It is hardly ever translated at all nowadays, as explained in the notes. 'Party of Wales' does appear as a strap-line on their web site, but that is all, really.
'The Welsh Party' would work grammatically but as far as I know it was never used for PC.
"The Party of Wales" still appears as a Hint, which is therefore wrong. If Plaid Cymru is never translated into English, then why is it here?