It seems perfectly possible. There doesn't seem to be any broadside example from before the 1820s (most are later), but that isn't such a very long time. Although I doubt if it could be proved one way or the other, further investigation (including any other ships called Princess Royal that were around at the time, of course) would certainly be interesting. I see from various website references (which I'm sure you know of) that Skinner died in 1832, and that there is a monument to him at Holyhead.