Is it commonly used in Britain outside the phrase “coconut shy”?
Not often. It can be used to mean a wild mis-hit, maybe in cricket, as in “taking a shy at [whatever]”
You have county agricultural shows?
This isn’t strictly true. Although they may share some lifestyle similarities with the traveller and Romani communities, funfairs and travelling circuses in the UK are run by ‘show people’. I only know this because I now live in a part of the country (Bedfordshire) that has a large number of show families living here.
Missed the edit window, but here’s a good article on travelling show life in the UK today (or 2012 when this was published 
):