EU B permit self-employed business; chicken and egg?

I am currently self-employed in a EU country and would like to start a self-employed business in CH. I am currently already in the CH within the allowed period that does not require a permit.

But in what order should I approach this? It seems a bit of a chicken-and-egg dependency between those:

1. The sole proprietorship business registration in CH.

2. The permit B for EU request.

3. A living address in CH.

Application for permit B (selbstandig=self-employed) as EU citizen requires to mention the employer in the CH.

But the employer is myself, so must I then register my business first? Can I register a business without being a CH resident?

No chicken and egg situation. Clearly described here:…EFTA_EU-8.html

Thanks. However, if I start filling the online form for SG kanton, I must fill in a company (Arbeitgeber) with company name (Name des Betriebes) already and I feel stuck in a chicken-egg situation. You suggest I go through the local authorities instead?