Luffy is clearly not hakiless rn. Go to any scene where he runs out of Haki in G4 and compare the large volume of Haki he exhumes from his entire body there, to the baby burp he let out here. If he's smart enough to know he can't beat Katakuri without Haki, why would he be running headfirst into two Yonkou in powered-up states?
Now that we've established he's not hakiless, I can't give a precise timeline but I'm under the impression they've been fighting for a while. Luffy's Haki definitely returned at some point and he's been contributing to the damage, whether that's by using G4 in bursts or through G2/3.
Why? Because Luffy states he's been to hell and back a few times now, indicating they've been fighting the two Yonkou in this state for a while. But BM wasn't in this state when Kaido first entered Hybrid. Hybrid Kaido is bruised, and the two most likely for this are Zoro and Luffy with Haki. Luffy says we've hit them so many times meaning BM has been hit too, but she was only hit once on panel - thus, she must've been attacked repeatedly off-panel. They've also been fighting for long enough that the SNs are wondering if their attacks are even working, which we know they were before the Yonkou powered up as Kid implied Luffy's Kong Gatling should've done a decent amount of damage.
Only way it's been ~10 minutes is if Luffy's Haki only recently returned, which I personally doubt as there was already a timeskip between Luffy running out of G4 and Kaido powering up, where we see Luffy looking completely exhausted. This would mean that in the time of say <8 mins, the SNs (and by SNs I mean Zoro) landed so many successful attacks to both Yonkou that the SNs started wondering if they were even working. Seems unlikely to me. They've been fighting for 5 chapters off-panel, that should be a decent amount of time.