Most of the ones I googled from this list speak German because it’s the most common language in Switzerland. Adding them in fills out the hypothetical, but really doesnt makes much sense.
Well, I didn't find any of the named not to be Swiss-German, or not at least closest to being so.
Moser and Daccord were the only somewhat shaky candidates. Moser was born in a town that is bilingual, so he probably has grown up this way and you could nominate him for "Team French" as well. Daccord's Swiss background is his mother's family, who comes from the French-speaking part of Switzerland, but this exact town has a Swiss-German background and he himself stated in an interview that it's important for him to continue speaking Swiss-German (additionally to English).
So for whatever reason, all of the Swiss NHL-players seem to have more or less a Swiss-German background.