I have a Savage 20 gage pump that I purchased around 1965. It has the screw-turn integral choke.
Was wondering if that choke can be replaced by a set of screw-in chokes and approximately what should I expect to pay for the mod.

No, it has to be cut off and threaded internally; it will depend on the thickness of your muzzle. Tru choke is the thinnest; Rem, Win, etc, require thicker barrels; cost; $100 to 200. Usually around 100.
Measure the O.D. of the barrel and then measure the O.D. of the tap. Subtract the O.D of the barrel from the tap and then divide by 2. This will give you the wall thickness after reaming.
For example; .850” barrel O.D. minus .814” tap O.D. equals .036”… Divide that by 2 and you get .018” wall thickness.

It is not recommended to perform this procedure where the wall thickness will result in less than .015”. Also, for a 12GA, you shouldn’t proceed in installing these chokes if the Inside Diameter exceeds .735” (.728” for thin wall chokes)

Easy to do an outside measurement, but I would need to cut the old choke off to do an inside one. I don't have an inside mike that would reach the 8 inches past the old choke to get an inside measurement.

Most shotguns will at least take a tru choke, and since you are cutting some off the muzzle, it gets thicker. I don't do chokes, but I am sure it will work. Unless the bore is already too big that is.

If it's a polychoke, leave as is.....they are not pleasing to the eye, but work great.

I would give Briley a call, their thin wall chokes can go into some pretty thin barrels, and the cost is reasonable.