I don't know that it's going to be a bad thing if your vapor barrier is on the inside of the wall. It's preferable it be on the outside, but it's easy to overthink it here as well.
Generally, when putting a wall together, you have (outside to inside)
- Exterior material (brick, siding, etc.)
- Waterproofing material (tar paper, Tyvek, etc.)
- OSB or other non-exposed siding
- Studs
- Interior wall material (drywall)
Your insulation goes in between the studs but, as you'll note, there's other material doing the water-resistance. Even if you mount your kraft batts with the tarpaper facing outside, the batts are simply butted together and stapled to the stud. If moisture gets there, it can still penetrate the studs (and it's unlikely the kraft paper extends down the the floor).
So why have kraft batts at all? You want to limit how much humidity reaches your interior side. If water reaches your drywall, all sorts of bad things can happen (chief among them mold). But that benefit is marginal at best for most people. If lots of water is making it inside your home, you'll have other issues, none of them preventable by kraft paper.
I have put the kraft paper on the inside without issue. Other sites, as well, have suggested it doesn't matter
As you can see, the permeance of the kraft paper rises as the relative humidity rises and hits 10, the point at which we describe a material as vapor permeable, when the RH is 60%. The upshot here is that if you put the kraft paper on the wrong side and it gets wet, it won’t trap moisture. The wetter it gets, the better it dries. If you put it on the right side, where the humidity is, it’s not much of a vapor retarder, because that’s where it becomes vapor-permeable.
I still want it on the outside
I would just stuff the insulation in, with the kraft paper on the exterior side. You can't have it perfect (stapled tabs to the studs), but I doubt it will make any difference.