Absolutely as wordstwice said. Don't worry! If you've got a degree then you've got more qualifications than a very large number of past, present and probably future ATCOs. What you studied is of absolutely no relevance, you'll be taught all you need to know about ATC at the college.
Have you considered trying another couple of airports, either NATS or non-NATS? It might be worth travelling a bit further afield if necessary. Although your success (or failure) won't depend on whether you've visited a unit, it'll definitely be a plus if you can, as you'll get the chance to see the job first hand and meet a bunch of fresh, enthusiastic / crusty, cynical (delete as appropriate...) folks.
It is a great job, best of luck with your application!