Snaring Foxes is a bit of an art, the height your setting your snares and the type you'd use, can, if not set correctly catch unintentional species.
Forking out for a trap isn't worth it unless your using it regularly. Both would be good to learn, you never know, maybe someone on here lives local and is willing to teach you?
Might be worth stating where you are in the country?
Probably quickest to post in the Firearms section and state where your from/area the permissions in and the problem your having. I'm sure someone will live fairly local and more than happy to help you out.