It's a pretty well known problem, opening the watch for the first time from the factory. Google it, and you'll find a few different videos. I think one guy used a large flathead screwdriver with the tip covered in electrical tape. The round-end of an old-school can opener seemed to work well too. I ended up using an old American dollar. My buddy used a Swiss Franc he had laying around, after a watch store gave up on it for fear of damaging the watch.
Whatever you end up using, use eletrical tape to protect the body of the case around the cover. You'll probably end up scratching the cover and asking Suunto for a new one, but you don't want the "opener" to slip and scratch the body.