Hi, John, and welcome!
I bought a sporter that had the '96 rear sight.  It wasn't adjustable for windage so I bought a 1902 sight to replace it.  You might know that the mounting hole spacing is the same for all the rear sights though the handguards are different.  Is your new Krag a sporterized rifle without a handguard or is it still in military configuration?  If it's still military I'd certainly keep all the original parts tucked away somewhere and use the replacement parts for shooting.
We'd love to see some pictures of your rifle!

To me, at least on the practice range, group size is, by far, the most important indicator of your, and the rifle, and the load, capabilities. Group placement (certainly important for matches and hunting) can come later - especially where any serious physical change to the gun may be needed.

I just know the collector's will cringe and cry out, but the only windage adjustment available with the 96 sight is to ever so slightly bend the front sight blade in the direction opposite the way you want the bullet to go.  I have done it, the steel blade isn't likely to snap.  Depends on how far off your are, but mine only took a few thousandths at most.  I used a small crescent wrench.  I am not responsible should you try it and break your blade though.