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: 
There are in fact [very few cases](https://english.stackexchange.com/questions/113774/why-do-only-a-few-english-demonyms-indicate-gender) where the customary demonym is *root + -man*— those you have named plus *Irishman*, *Norseman*, *Welshman*, *Scotsman*, and (obsolete, now considered offensive) *Chinaman*, and maybe a few others in Britain like *Yorkshireman* or *Cornishman*.

In the absence of a more established form, the [demonym](https://en.wikipedia.org/wiki/Demonym) is usually the same as the adjectival form. Just as we would speak of an Indonesian, an Omani, or a New Zealander, we would speak of a **Swiss**.

It sounds abrupt, even to this native speaker, not only because it is monosyllabic (e.g. calling someone *a Japanese* also seems off), but because in today's politically correct age, referring to someone solely by their nationality or ethnicity is potentially problematic. It would be preferable to use the demonymic adjective in conjunction with a noun; *Swiss man* would suffice.
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.