Aparently there was a partner party established with a different name in Switzerland pretty early. A.H. in July 1932 in Radolfzell/Germany was giving a speech very close to the Swiss border to some 35,000 locals incl. 5,000 excited Swiss. Stefan.
Looks quite interesting. A MASTERABLE PAST? SWISS HISTORICAL MEMORY OF WORLD WAR II https://scholarworks.uno.edu/cgi/viewcontent.cgi?article=1003&context=honors_theses