I never knew this. During World War II, about 2,200 Swiss volunteers served in the German armed forces or SS. Some of these later numbered among the three and a half million German prisoners of war held in the Soviet Union. Their stories are told in an exhibition at the History and Folklore museum in St Gallen. It’s called Cold, Hunger, Homesickness—Soviet War Captivity 1941 - 1956. WRS | The Swiss who fought for Nazi Germany
They were probably among those nordic volunteers to the Waffen-SS divisions like 5th SS Wiking, etc. Pretty hefty price to pay for wanting to "join into" the fun!
Switzerland was a strict neutral during WWII, but although it avoided openly siding with either the Axis or Allies, a small number of Swiss citizens without offical approval did actually volunteer for service within the German Wehrmacht. In fact, between 700 and 800 Swiss volunteers are known to have been incorporated in the Wehrmacht during WWII. Of these, at least 300 are thought to have been killed in action. No single unit of Swiss volunteers was formed during WWII though, and all volunteers served on an individual basis within the Wehrmacht. The vast majority of Swiss volunteers were accepted into the ranks of the Waffen-SS, notebly in the 5.SS-Panzer-Division Wiking and the SS-Standarte Kurt Eggers. Feldgrau :: Swiss Volunteers in the German Wehrmacht WWII