Swiss companies paying non-residents?

Hi all,

I'd be grateful if someone could help me out with a hypothetical situation, because I can't find any specific information on this on the internet (and my German is terrible).

I used to be a Swiss resident - I'm not anymore. However a company I used to work for in Zurich is still interested in having me do some part-time occasional work for them - software development specifically. It would not be more than a few days' work per month (e.g. some months I might charge them 500 franks, other months 1000-2000). Since this is software development, I can do it remotely, without any need of actually being in Switzerland.

Now, I would be in this capacity just a private person, a freelancer (I have no registered company or any other legal entity) so there would have to be a contract between me, Joe Public located outside of Switzerland, and Swiss Corporation AG from Zurich, I would send them an invoice each month, and they would wire the funds to my non-Swiss account.

Question: is this actually legally possible? Since technically, I would be working for a Swiss company as a private individual, but without having any residence/work permit or anything.

The extension is, if this is possible, does the Swiss company have to pay some kind of withholding tax on what they pay me? All I could find on the internet regarding withholding tax for non-residents is about income derived from dividends, pensions, or rents on property owned, nothing about income for services rendered.

Or is this impossible, and I have to have a registered company in my country of residence to do business with a Swiss company this way?

Thanks a lot...