It could be intertwined with Shanks. Or it could be intertwined with the other members of Cross Guild.
I'd be nice to get at least short flashbacks for all the heads of Cross Guild. Mihawk, Buggy, and Crocodile. We still have pretty huge gaps in the history of all three of those guys. So, I could see us getting at least a short series of flashbacks where each of them get a flashback. At least for a chapter each or so.
Of course....two out of those three guys DO have ties to Shanks. Both Buggy and Mihawk could be explored in a Shanks flashback. And...I don't know, maybe you could say Crocodile has a history with Garling or Shamrock, in order to work him in, too? Maybe Ivankov saved Crocodile from Garling, back in the past, and that's why Crocodile owes Ivankov? Which could potentially let Dragon show up, too. Add in a little bit for Blackbeard and maybe a bit more for Roger, too, and Shanks' flashback could be pretty substantial.
So...yeah, I could see a Shanks flashback covering a lot of this ground. If used efficiently, we could fill in a lot of gaps for a lot of characters. And it'd make sense to do it, if we see Shanks fight Cross Guild or Blackbeard in the future.
As for who else could show up in a Mihawk flashback...well, we don't actually know that many swordsmen, really. I guess it might be a chance to showcase more of Zoro's family, if they have any connection to Mihawk or if Mihawk ever went to Wano. Mihawk does have very similar eyes to Imu, so there is a chance there's some sort of connection there. Even if it's just to some other God's Knight. That female God's Knight who's always by Garling's side in the God Valley flashbacks actually seems like a decent candidate to do something interesting with.
But, I imagine that if we got a whole flashback centered on Mihawk, most of the characters who showed up would be completely original. Some Marines, just so we could see how he earned that "Marine Hunter" epithet, but I'm not sure it'd be anyone we know. And I imagine we might get to see Mihawk's master, whoever taught him how to be a swordsman in the first place. I imagine there could be a sword-smith in Mihawk's past. Maybe some sort of pastor or other religious figure, since Mihawk does keep a cross on him. But, outside of maybe that, I'm not sure who else could show up.