Degree isn't always necessary.

"Admissions are limited to managers, specialists and other qualified workers. ‘Qualified workers’ primarily means individuals with a degree from a university or university of applied sciences who also have several years of professional experience. Depending on the profession or the field of specialisation, individuals with special training and several years of professional experience can also be admitted."

https://www.sem.admin.ch/sem/en/home....html#Personal requirements

If you can fill that niche then you may have a good chance of getting a permit.