Switzerland was neutral in WW2. There would be less fighting or interaction with soldiers if Italy crossed through there, as opposed to France or Austria. It’s the safer route, as Switzerland can only threaten to shoot, but won’t actually if he wants to maintain his neutrality.
Yes, Austria was Nazi-occupied and was on the Axis’s side, but Italy doesn’t like fighting and probably didn’t want to encounter any of it. Hiking over mountains would be more preferable than having to potentially pass through active battlefields.
