Its a couple of years since I was a dispatcher but it seemed that most people started out part time on a temporary three month contract and were either retained or binned depending on weather they were any good. I cant imagin Servisair offering any form of weekend work. I dispatched for a couple of months one summer during my degree when I didnt have any lectures but you may be able to arrange your shifts around your degree. Saying that you will be asked how flexable you will be to working extra hours/ covering shifts etc. so it might be worth keeping your degree under your hat for now.
If its weekend work you are after then one of the flying schools would probably be able to accomodate this. Both multi and LFS work 7 days a week and probably have a different set of staff at the weekends to those during the week. Also, weekends at a flyng school may be more hectic than during the week due to pleasure flights and trial lessons etc.
In the final year of my degree I managed to hold down a weekend job at one of said flying schools with little interference to my studies.
good luck
ram