Hi,
There is an endless amount of information available on-line, but it's not always easy to understand what is true.
You'll find thousands of "incorporation" websites with contradictory information.
I've been trying to "see trough the mist"

myself as I'm planning to create a company...
Anyway, as far as I understood, (not guaranteed information) an US LLC might be a good option, because such company is not teated like a "company" for tax purposes in the US, it is rather a "flow-trough" entitie, being the beneficial owners taxed on their share of the profits and not the company itself.
When you say " One concern is that I might run into problems, because the company would not be liable to any Swiss company tax"
you're making it more complicated than it actually is. An US (or any other foreign) company cannot, by defenition, be liable for swiss tax. Swiss tax applies to swiss entities (companies or individuals). The fact that your US LLC is not liable for Swiss tax is an enormous advantage. But, you, as a swiss resident are required to declare your share of the profits from such company and pay the tax (Income tax) here.
One other thing you might want to consider is the US tax liabilitie.

It all seems very simple. Your US LLC is not liable of US tax, because it is taxed as a flow-trough entity, then; being you liable for tax purposes, not in the US because you live in Switzerland then; only tax liable in Switzerland. Fine so far.

In theory it would be easy not to pay any tax, like many non US people do trough US LLC's: just simply not declaring their profits in their home land.
It seems not to be the case here, but it doesn't really matter anyway.
So, fine so far, concerning taxes...
There is an if though: to keep it this way your US LLC shall not sell or buy in the US or do any relevant business in there, otherwise you will become US tax liable in what concerns the profits generated in the United States or even all the profits generated trough your US LLC. Then you may know what follows: potential double taxation, having to claim tax refunds or exemptions when tax treaties apply, etc, etc more papper work and less money left; meaning - unless you're expecting some reasonable amount of money from this venture that would make this scenario worthed anyway - (unless that I say) what you're saving in tax and swiss bureaucrats you'll spend in american laywers and tax expert accountants.
Conclusion: an US LLC might be a good option if you don't plan to sell in the US.
If you do, then probably other off-shore jurisdictions are more suitable.
Using offshore companies doesn't mean you are incurring in tax fraud: as long as you declare your revenues to the Swiss taxman, everything's fine

.
That, being said, you can incorporate a company wherever you like (as long as the locals allow you, the Swiss won't care). You may prefer other countries for commercial or other practical reasons like how business friendly they are, how easy is to do business there or with a company registered; and of course what corporate tax rate they offer.
You have good jurisdictions available if you want to do business with europpean countries, like Cyprus, Ireland, or Madeira.
Costa Rica seems to be great too, if you're not especially into europe, and it's not black-listed

Then you have the "hardcore off-shores" like antigua, bermuda, etc.
You can chose Singapore or Hong-Kong because they are very business friendly. There's a lot of possibilities; avoiding tax is not based on where you locate your company but on your choice of doing it or not!