RE flight schedules, why a flight from London? Besides the boat option, why not fly from Hawai’i around the other way, changing planes at other friendly places? [not sure of the max. long-haul flights at the time.]
I'm not finding many options to fly out of that area in 1961. What I've found so far is BOAC and East African Airways serving that area, and both had London - Nairobi flights. According to this, the farthest east they went at that time was Bombay.
When I look on expedia for Honolulu-Nairobi flights, the stops are all in Europe - Amsterdam, London, etc.
As for ships, I doubt there would have been any direct service from Hawaii to Nairobi. The closest I can find is 15 days from Honolulu to Manila, on a luxury liner that would have been new in 1962.