Sooner we show Shikai sooner we can ask Ichigo why he can't do it?
"You can't hear my name yet? And I am not 'reading your mind', as trite a way of phrasing it that is – I am part of your soul, it is only natural that your heart and mind are open to me" she huffs,
"…so since I have Rukia's powers, I have to do her job for her until she gets them back" he finishes his tale.
Karin's zanpakuto is part of her soul while Ichigo is borrowing Rukia's power. Karin has enough information to deduce why he can't do it.
Besides is that worth drawing the attention of Soul Society before canon?
"You should be careful about calling your zanpakuto's name carelessly, Kurosaki-san – it might attract the wrong sort of attention."
Is it worth the risk? You don't know what sort of attention it could bring down on you or your family – you can beat this thing without Nejibana, but you're just not sure if you can do it before Ichigo gets here, the idiot.
Even if it'd be a more certain matter – that shopkeeper's words haunt you; you'd almost never seen him be so serious in the short time you've known him. Something that can make that guy stop smiling isn't anything you want to draw the attention of.
I'll note you've already asked about why releasing Shikai is dangerous, and he just told you that Soul Society doesn't approve of shinigami existing outside its authority, and Shikai makes them much more likely to notice. I was going to have it appear in a flashback at some point but there's no harm in telling you now
Changing vote to:
[x] Hit and Run. Keep their attention with hit and run tactics, only going for a decisive strike once you have an opening from Rukia.
-[x] Karin focuses on keeping the Hollows off Rukia, Rukia focuses on Kido.
--[x] Keep their attention on you. Use taunts and frequent enough attacks to keep them from being able to outright ignore you to go after Rukia instead.
--[x] Try to move the combat closer to the direction Ichigo will be coming from.
--[x] With you holding them at bay, Rukia can focus one down at a time. Assist if you see an opening, but prioritize holding them off.
--[x] If you get openings for clean attacks, prioritize disabling their ability to attack from range and disabling their mobility.
--[x] If Ichigo makes it there before you two finish them off, get him to help Rukia focus them down one at a time. He's liable to charge in face first like an idiot, which may present extra openings to take advantage of.
---[x] Don't let him get smacked around just because he charges in face first. If there are still two up, make sure the one he isn't hitting doesn't take advantage. If there's just one, keep it from getting a clean hit on anyone.
[x] No, keep your sword sealed.
I removed the
--[] Use terrain to your advantage. If Rukia can get to safe, high ground, that's where she should be. If you can use tight spaces to make it more difficult for the hollows to maneuver, do it.
and replaced it with trying to move the battle closer to Ichigo is coming from.
If Rukia is on high ground and Karin is in relatively tight space won't that limit Rukia's ability to assist?