263 sqn converted in Dec 1940, if FC wanted to be rid of them they could possibly arrive in Takodiri to transit Africa in Jan or Feb 1941. 137 sqn converted in Sept 1941 so could be in Egypt before the end of 1941.
I think there would be plenty of opportunities for long range Whirlwinds to contest airspace that IOTL were left to the Germans. They would have a field day against the Ju52s that dropped paras on Crete.
Just as a bit of thread drift, WI Whirlwinds were sent to Singapore?