The British sail on from Copenhagen and bombard St. Petersburg. They've already forced the surrender of the Danes, sailed a fleet into the Baltic, and were on the way to Russia when Paul was killed.
The difficulty is that all the social unrest and alienation of the nobles and military that caused Paul's death in the first place still exists. Avoiding one attempt on his life doesn't really improve his situation. I'd give it pretty good odds that somebody else assassinates Paul. Considering that the assassins weren't punished at all in OTL it seems pretty clear that Paul didn't have much support or popularity.
He either has to continue his association with the military and nobles who seem to want him gone or isolate himself with loyal but not very influential supporters. Neither is a good option when trying to fight a war against the British.