Howdy Rob.  Welcome to Parallax Bill's Yugoslav Mauser forum!

First question;  Have you thoroughly cleaned and degreased it? These rifles were usually slathered in cosmolene and had about 60 years of absorbing the stuff.  Just wiping it off won't get it.  If it's there, we can tell you how to clean it if you don't know and and/or haven't done.

I assume you are not using Formby's or any other such since you specified "pure tung oil." 
Second question; Do you mean literally "pure" tung oil, no driers added?  That will not really dry or cure like blo.  "Boiled Linseed Oil" (The closest thing to what the Yugoslavs actually used on their stocks.) is a pure seed oil that has had chemical driers added to hasten the curing process.

In either case, what you'll want to do is rub in the oil working it into the stock by hand or rag for about 20-30 minutes. Let it stand another 10-15 minutes then giving it an overall rub down with a clean dry rag.  The idea is to only leave the oil that is IN the wood and not any layer lying ON it.  Do this a minimum of 3 days to a maximum of 10. Three days to a week is average, it just depends on how dry your stock is.

There is an old rule of thumb for such oil finishes:
Once a day for a week,
Once a week for a month,
Once a month for a year,
Once a year thereafter.

Remember, unlike the gunmakers of old, we are just trying to protect the wood, not build a shine onto it.  To suit our purposes, a simple working as described for 3 or 4 days will replicate a military 'finish.' Just give it another rubbing whenever you have cause to clean the rifle like, after shooting or say your 'yearly' (or whatever your normal routine) cleaning. Not "too extreme" I'd say?  If you hunt with it or otherwise take it out to shoot or hunt in the weather, give the stock a good oil rub down when cleaning just like you do your metal.
As for "original military finish" the Yugoslav soldiers were known to use old motor oil in the field as did their German counterparts or predecessors of either forces in WWII.

WARNING! Do not throw used rags into a closed container!!! --- They can spontaneously combust and start a fire!  Make sure to hang and let rags dry before disposing of.

Concerning the handguard, it sort of depends on the wood. If it is walnut as is the stock, then a little simple staining can match it up.  If it's a later elm replacement, that's a little tougher to match.  You can still stain it but, often times the grain is just too different to match.  Abut all you can do with that is try to find a replacement.  Oh there ARE things you can do, such as imitating a walnut wood grain pattern by burning with a soldering iron or 'painting' such on by denser applications in specific areas or using darker stains 'painted' on with a very stiff brush to imitate grain lines... but, now we may be entering the realm of "extreme?"

See the rifle below? Note the grain on the handguard. It is elm but, the grain was not an impossible mismatch so it was just stained to match.  I also scrubbed it out thoroughly and added  a touch of bleach to remove some of the tell tale redness.
The stock isn't fancy finished, that's just flash reflection.