A largely Romance speaking Switzerland

My apologies for not quite following the OP. Did you mean Romansh (the rare and unique Swiss language) or Romance (the entire language group, including Italian and French)?
 
I'd say it's theoretically plausible. Swiss forces were used throughout Northern Italy as mercenaries during the Early Modern era. Their last significant expansion was when they grabbed the Italian-speaking canton of Ticino from Milan. They actually managed to conquer a good deal more of Milan up until losing the Battle of Marignano to the French in 1515. Lombardy today has 9.7 million to Switzerland's 7.7, so grabbing a significant chunk of it would probably result in majority Italian and French-speaking Switzerland.
 
This argument rather seems to lead to more German speakers in today's Italy, no?

No. With a few exceptions like the Hungarians, generally speaking invading forces aren't very good at imposing their language on a much vaster majority. Add to that the Swiss mercenaries, even if they settled in Lombardy, probably wouldn't bring wives along and would marry Italian women. You'd just end up with a lot more German surnames in the region.
 
Try a much earlier POD. In 496 the Alamanni were defeated by the Franks in the Battle of Tolbiac. Now imagine that the Alamanni win this battle and stay victorious the following years. They don't feel the pressure to move south and stay where they are (north of the Rhine). At that time the population of Switzerland still consists of thoroughly latinised Helvetians and is concentrated in fortified settlements left behind by the Romans one hundred years earlier. The Helvetians are able to keep their Gallo-Roman culture intact in the northern lowlands and start re-expanding into the Jura und the Alps.

In OTL the Alamanni (under the overlordship of the Franks) ignored the existing settlements at first and settled in uninhabited areas in the eastern and central parts of Switzerland. The cultural assimilation of the Helvetians was a process that took two to three hundred years. In western Switzerland (then dominated by the Burgundians and today French-speaking) the assimilation process went the other way round.
 
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