What if Russia lost the Alaska panhandle to Britain before they sold it Alaska to the USA?

As the title says:

Lets say, during the Crimean War, a Royal Navel squadron sinks/capture a Russian ship or two in that area and do a bit of "fighting" and capture a fort in the area. All and all not much fighting be enough to get noticed back in London and Moscow.

During the Treaty of Paris, Russia does not want to give up all of Alaska so they are willing to lose the panhandle and all the islands in that area as well the border moves 1 deg west all the way to the ocean.

Would the USA protest the transfer as per Monroe Doctrine or would that not count?
If they did protest what could they do to Britain?

Would Russia want to sell Alaska sooner else they lose the rest of it due to treaties or other reasons?

Would the USA still buy it?

If there was no panhandle how or would the Oregon Crisis happen?
This POD doesn't seem implausible and it's one I haven't seen before. Interesting.

I'd like to see the different points of view as I researched Russian Alaska a bit in a thread asking what the largest extent of Russian colonisation of North America might be.