In Bolt Action Rifles, Mr. De H. makes a point. Nothing you do now adds anything to steel made in 1900 or
Sure the gun was "re worked' in 1938 for use by a soldier considered expendable, but when was it made? I would pull the wood and study the metal for date of manufacture and/or date of proof. Mr. D mentions seeing bolt set back when pre WW I Mausers were rebarreled to more modern pressure cartridges, i.e. .243 W.C.F. --Made after 1930? Alot less worrysome.
Super quick/ super easy, find someone with an 8mm/'06 reamer and re-chamber. '06 is 63mm long and 8x57 is 57mm long. This should "clean up" the chamber, throat, etc. unless the bore is pitted, rough, NRA "moonscape..." And perform like a .35 Whelan or close. Dies are available from ch4d.com, huntingtons.com, and others.
I don't understand your comment on barrels. Give a barrel maker the outside diameter of the front ring (where the barrel screws in) and he can tell you what you need for a barrel. Add maker and he will tell you the exact threads. No need for cutting up a large ring barrel unless you really want to for your own experience. If they make "large ring" barrels, chances are they make "small ring" barrels too. 93's and Swedes were "small ring."
From there it is what you want and budget allows. Variations on wood or plastic are endless. I suppose you will drill and tap for scope. Hardly rocket science. Enjoy. and luck.