8x68S has OAL of 3.425" while 404 Jeffery is 5.35" long. 404 fits into a standard 98 Mauser after opening the bolt face, changing the extractor claw, moving the loading ramp forward, widening and lengthening the bottom metal, and of course modifying feeding rails. No need to move the ejector or carve away locking ring (e.g. fitting 375 or 416 Rigby in standard 98 action). I guess it depends on what one defines as "significant". As I understand it, bolt face on 8x68S would not require opening, the extractor would also be unchanged, and I doubt the loading ramp would need to be moved much if at all. Would not need to touch locking ring or ejector. Some modification would obviously be needed to bottom metal to handle the wider shoulder. Not a big deal.
Edit: Probably little if no modification needed for bottom metal. The 8x68S has a narrower shoulder than 30-06 which is easily fitted into standard 98 Mauser. The 30-06 has a slightly shorter OAL, just 0.08". And 8mm Mauser is slightly shorter than 30-06: 3.228" vs 3.34" 30-06 vs 3.425" OAL for 8x68S. I would not hesitate to build one of these on a standard 98 Mauser. It would be a fun project for a beginner. The cartridge does have a rebated rim but so slight that I suspect little probability of encountering the usual feeding issues.