Great Britain attacks Russia in 1801

What would happen if Tsar Paul had been overthrown and killed a bit later than OTL, long enough for the British fleet under Parker and Nelson to perform a Copenhagen on the Russian Baltic fleet?
What makes you sure the British could pull off a Copenhagen? I suspect the Baltic is a bit different than the Atlantic, and IIRC the Russian fleet and St. Petersburg's defenses were nothing to sneeze at.

But ya, Britain is probably now fucked.