On the contrary, his Dracule surname is quite apt for what he is. His eyes are telling, too. Him and Imu are the last descendants of the Ancient Kingdom's vampiric clan, the ones who worked from the inside with the 20 Kingdoms and backstabbed the AK. They have longer-than-normal lifespans, even exceeding that of a giant. Imu reflects the more negative connotations of the clan, staying in the shadows, manipulating people to do his bidding. Mihawk, on the other hand, knows no allegiance. He merely sails the sea in search for a good fight. He might as of late calmed down, even getting cozy in a combat-less lifestyle, but his thirst for blood (figuratively; I'm not saying he'd pull a Stussy and bite people's necks) is still bubbling right under the surface.
For Mihawk to be Rayleigh's son would be to reduce his importance in over all worldbuilding lore. He is part of the Void. He is a Zunisha in human form, wandering incessantly.