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: 
I'm Swiss and this has never occurred to me until I read "a Swiss" in an article earlier today. It really does not sound right. If Shakespeare really referred to them as "Switzers", that seems good enough for the rest of us. My suggestion was going to be "an Helvetic" or "an Helvetian", derived from the latin name of the country (Helvetica, which is why the initials of the country are "CH" and why the currency is "CHF"). It may admittedly not be intuitive or obvious to readers, so perhaps this suggestion isn't the way to go.
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).