You fight with a blade = swordsman
You fight with a gun = sniper/gunman
You fight with your devil's fruit ability = ability user
You fight with a weapon = "that weapon" user/fighter
You fight hand-to-hand = brawler
You fight with Haki = Haki user
Marco is an ability user, Haki user, brawler, don't know if he can use a weapon
Big Mom is an ability user, Haki user, brawler, sword master, a meme
Teach is a double ability user, brawler, fought and scarred Shanks with his particular weapon, can use a gun, don't know if he's an Haki user but I hope so
I see this thing like a multivariate spectrum, representabld by a radar chart, with the single values for each variable and a final overall.
And know, let's talk about Mihawk and Shanks!
Personal opinion: In swordsmanship, Mihawk is a 98/100, Shanks is a 94/100 (atm, the 2nd best Swordsman in the world), Haki use goes like a 95/100 for Shanks (atm, the most impressive user alive) and 92/100 for Mihawk.
Overall, they're like Akainu and Aokiji, I guess that after a 10-days battle the WSS will prevail, anyway, because Red Hair didn't show other abilities to compensate his inferior swordsmanship and, notably, he has a significant physical disability in combat.
So, to put it simple for those who doesn't want to read all this shit: Haki man don't apply to anything we saw so far, it's not a category per se but just apply to any combat style.
Ps. If Mihawk or Shanks had ate Gura-Gura or Magu Magu, they would have been the "world strongest man", they're unbelievable, the references for the future Pirate King and his first mate, so enjoy these 4 characters and stop being childish, thanks