Just reading your post i can see that you have done you research into the companies and would really like to become a dispatcher.
However the reality is you must start off as a ramp agent or up at check in for some time in order to gain a much needed airport experience, many people dont appreciate how many activities go on in order to keep an airport or airline running.
From then you will have your foot in the door and should a dispatch position come up you can go for it. but also dont forget there will also be other people there that already have their foot in the door wanting the same position.
Im not trying to put a downer on it more a true reflection of how it happens. Swissport is a very good company to work for and there are plenty of opportunities when you get there.
Hope this helps you in some way and if you want to ask any more questions then best to pm me