Looks like a Redfield mount. The old school vertical split rings are not cheap.
Redfield Pre-War 1 Scope Parts at GunBroker.com : 848852900
You might have to be conscience of how the rings mount on the scope(if you went with a K4) Not an expert, but unscrewing a scope lense might be necessary to slide the rings on. Not sure if stretching the rings open is recommended.
A Lyman Alaskan is 7/8" tube, and horizontal split rings might be necessary.
I would try and go with blued rings, to match what you have.
Mike