Hi Judy -
I've just looked at the National Archive - and there are only two Wilfred Cater entries for the period 1914 to 1945. One of those is for a Wilfred W Cater, the other, plain, Wilfred Cater. Here is his entry:
Medal card of Cater, Wilfred
Corps: Machine Gun Corps
Regiment No: 137162
Rank: Private
It's could be your man ... there aren't any others !
Also - did you look on the extra details pages of the CWGC e.g. the cemetery details pages ? I note that one entry confirms he was a pilot. The detailed entries for Barnstable cemetery show that there were very few RAF casualties buried there - which suggests that it wasn't near a highly active base, and none for crew who died on the same day - so he could have been a fighter man or simply brought home to be buried.
Not a lot I know - but a bit more to puzzle over.
Aye
ME