Hello Gordon long time no hear!
Great badges you have there... The cap badge was definitely worn as an arm badge and not the collar badge as some people seem to think. I have reams of photographic evidence and a whole host of variants including one cast in solid silver made by Wew & Co (a now defunct jeweller from Brum). I also have a number of home made items as the badge was never officially sanctioned as an arm badge and therefore never manufactured for issue or sale . All of them have lugs or an excuse for lugs.... I have none with clasp fittings... then all of a sudden you find 3....I have to say though i am sceptical... I think they would have been a really 'sloppy' fit on the uniform and i tend to go with what Alan said. There are loads of brooched badges (collar type) in the museum, but no cap size badges... But hey!! Who will ever know... anyone that might have been able to say "yes my arm badge had a clasp" is now gone just like the guys who wore it with lugs... I certainly wont die in a ditch over it.... Maybe you can sell/trade one of them with me?
Regards Howard