Another angle is that the British too were interestend in buying Alaska. But their interference in the Crimea meant that their offer was not seriously considered. Russian diplomats feared Alaska would make an arch enemy stronger.
In time, Alaska would have probably been incorporated into Canada.
The 1903 Alaska boundary dispute was settled politically. The British sided with much of the American claims, not because of the merits of the claim, but the British owed or needed favors from the Americans. Canadians were upset: that was the start of breaking the cultural hold Britain had on Canada.