You stand a very good chance of being pleasantly surprised how well those replacement barrels line up, and headspace perfectly.
I just found a Norwegian 30-06 replacement barrel for their conversions of captured K98s left there after WWII and their subsequent adoption of the 7.62x63 aka 30-06, there weren't any sights installed as it was new in the wrap, old stock, made in the early 1950s.
In truth, it doesn't shoot as well as the German barrels, chambered for 8x57 and it seems to be a fouler. The German barrels usually have mirror polished bores, but even though the Norwegian barrel as identical exterior dimensions the bore appears to be cut rifled and there are some very fine chatter marks. I'm going to firelap it and hopefully that will smooth things out and help it to shoot better.
The only time you have to worry about a K98 barrel indexing properly is if it's a "take off" barrel. The sights are soft soldered in place and aligned after the barrel is installed. Both the rear and front sights are mounted on a "sleeve"
I bought a bunch of "surplus" Israeli 7.62x51 barrel around 1985. International had a few hundred of them and I was lucky enough to get a very good buy on them, if I took all of them, which I did.
It was a great deal for me. Surplus 98 actions and and those chambered for the 8x57 were "cheap" People, those that hunted especially didn't want Mausers which had been sportered or had them tucked away in closets, because soft point ammo was not always available.
Because I had been lucky enough to pick those barrels up cheap, I could do the conversions to "308 Winchester" 7.62 Nato for a very reasonable price.
I even bought a 7.62x51 Palma Match reamer to ensure headspace was right if it was necessary.
I only used that reamer twice, and it wasn't because the headspace was out of spec. Two shooters wanted rifles chambered with Palma Match for one of the competitive venues they pursued.
Some of those barrels shot like lazers and some were "acceptable with factory ammo.
AL, I didn't see if you mention if your replacement barrel is a take off or not. If it is, and still retains the sights a smith will have to either melt the solder to turn them into top dead center alignment or he will have to set back the shoulder and the face of the breech face enough to get it to tighten up at TDC, and very likely have to recut the chamber.