"The British Isles" is a geographical term for the various islands offshore from mainland Europe. Not everywhere is "British", a political term. Most notably, the island of Ireland is divided into the Irish Republic (26 counties) and the statelet of Northern Ireland (6 counties).

"Britons" might do but there an awful lot of Northern Ireland residents who would object for historical / cultural reasons, as would residents of the Isle of Man and several Channel Islands.

I'm an ignorant lout too as far as pubic wigs are concerned. Never heard of them, nor can I imagine their purpose. Are they the same as fig leaves?

"Murkan" is a fairly widespread (even if the contributor from Virginia has never heard it) term for an American, based I would imagine on how many of them pronounce it. It is not especially derogatory, if at all. Surely you wouldn't prefer "Yankee"? This would surely disenfranchise all those resident south of the Mason-Dixon line.