So historically (though less so lately) "man" would be the unmarked word, and "woman" is marked. Is that the right use of the word?

Yes. But, earlier in English, there was a complete set of words like those in Latin (homo'human being', vir 'man', mulier 'woman'): Old English mann 'human being', guma 'man', and wīf 'woman'. Ironically, guma is related to homo, the generic term in Latin; it is also the origin of the groom in bridegroom. OE wīf is also shows up in a compound wīfman which is the origin of woman.

Ceci n'est pas un seing.