Some interesting and informative posts here.

Switzerland is quite a desirable destination on the international teaching circuit. If you wish to obtain a teaching position here, my advice would be to proceed as follows:

It is unlikely that you will obtain a tenured position as a coach without a teaching qualification. Schools make a distinction between someone who is a coach and someone who is a teacher (I am not going to comment on whether this is right or wrong - it is just the way it is). So what do you do?

1. Decide what it is that you really wish to do - teach or coach (by teaching I, of course, include PE teachers).
2. If you wish to coach, then gain some coaching qualifications and be prepared to move around to coach in 2 or 3 schools a week.
3. If you wish to teach, then try an get another string to your bow. You have a masters level qualification in Management, so would you be able to teach Business and Management at the IB Level? If so, then start looking at offering this at your current establishment.
4. Look into studying for the iPGCE (or local equivalent). This will give you the pedagogical qualifications that are required to teach at most of the better International Schools.

If you do not fancy going down the pedagogical route then give teaching a miss.

Good luck.