In order for a business to have a permanent establishment in country A it has to register a branch there and carry on business there. If the business is buying and selling financial instruments on international exchanges via a company registered in Switzerland and a stock broker registered in the US, article 7 won't apply for Hungary.
Why do you think in the DTA between CH and HU they differentiated between a place of management and a branch?
Because you can have a place of management without a branch so a PE could be created even without registering a branch.
Also it's in OP best interest to create a PE in Hungary because HU levies 9% taxes instead of ~12% (depending in which canton the company is formed) in CH.
No dividends but wouldn't the DTA apply to regular business income too?
DTA only applies to dividends, interest and royalties.