Question: So we call a French male "Frenchman", an English male "Englishman", and a Dutch male "Dutchman". what do we call Swiss males?

"Swissman" comes to mind, but it sounds like a cheesy version of Superman, like "Cheddarman" or "Mozzarellaman".

Answer: 
Whichever the nationality, it is an Adjective in a Noun Phrase, whether you tag on a denominator or gender or other such noun. 

So, "I'm a Swiss (man / woman / citizen / denizen / etc.)" is fine. Or then simply say, "I'm Swiss" leaving out the [indefinite] article. 

(Please do post a comment if you don't agree with me).
I agree with the above; however, another alternative might be "man from Switzerland".