I don't know, depending on the exact route you barely ever go more than 10 miles from land. As long as the weather is alright I could probably consider kayaking it if I had some time to prep for the trip. I know people kayak way more distance in a day but I would probably split it, sleep/rest on one of the diomedes. Looked up the currents involved and its not much of an issue based on a live map right now even for kayaking. So even a fairly small boat should be perfectly fine.

I guess it depends a bit on how much if any effort is put in to stopping people crossing the border.