I think that's obvious. If we're being deadass he probably pulls a random blade out which is black like the DR weapons, I wouldn't get my hopes up on random Mihawk lore.
I dont think its obvious they arent. Imo more things point out to them being at least related vs not atm
- Same red/circular eyes
- Dracule/Dracula has demon/devil connotations and Imu literally is the devil
- Mihawk having a rivalry with Shanks, a Figarland
- Now Imu creating a Yoru-like blade and apparently fighting "like" him (ill wait for raws)
I think its safe to say that pretty much any endgame relevant current/modern character seems to have some sort of special lineage (Luffy, Dragon, Shanks, Shamrock, Teach) and I dont think Mihawk is an exception here.
I also struggle to see Mihawk's endgame relevancy if he's not, at least on some level, tied to other endgame antagonists. I absolutely do not think he's immune to this.