Your company will still need to go through the non-EU hiring process to prove they can't find a Swiss/EU national who could do your job I'm afraid. Nor could you transfer it without a new employer having to do the same thing as your permit will be tied to your company I assume. https://www.bfm.admin.ch/bfm/en/home...zulassung.html
Some other points to consider. http://www.kmu.admin.ch/kmu-gruenden...x.html?lang=en
Only holders of a valid C permit (settlement permit for third-country nationals), the spouse of a C permit holder or the spouse of a Swiss citizen have the legal right to establish their own business in Switzerland.
All other persons have no legal right to set up their own business. They must submit an application to the respective cantonal authorities.
Apart from the necessary personal requirements, it is decisive in the evaluation that the company will have a "lasting positive effect or influence on the Swiss labour market".
Did you submit an application to be able to set up your business?
Limited liability company (GmbH)
The limited liability company (GmbH) as a legal entity must be represented by at least one person resident in Switzerland. This can be the manager or a director. Accordingly, this person needs to have a valid residence and work permit in Switzerland.
Given that you were both students did your permits include the right to work as far as the terms for setting up a GmbH are concerned?
Note that owning/investing in a business here as a non-EU national does not grant you residency rights.