I have 3 Brazilian contract DWM Mausers, one is a carbine with 20 in barrel, very handy woods gun. Great guns for a great cartridge. So strong an action that I accidently put a .308 Winchester round through the carbine, no problem.
I also have a Ruger 77 with the skeletal type stock with a Springfield armory 6 power on it.
The 7mm Mauser has taken a few Elk and deer with no problems. One shot DRT. 170 grain bullets, have great ballistic coefficient and sectional density. If it was good enough for W. D. M. (Karamojo) Bell , it's good enough for me.
Easy on the shoulder too.
Your Mausers have 98 actions, big difference between them
and Spanish made pre 98s. Ever read the story in the AR
magazine about the guy who sporterized his Arisaka and
used it for deer hunting? He knew conversions to 30-06
were popular so he rechambered his rifle to 30-06.
Used it for a while and took one deer with it. The brutal
recoil got to him so he had a gun smith look at it.
The owner was none too bright the gun smith discovered
because the Arisaka was a 6.5 mm not a 7.7 mm. Yep
factory 30-06 ammo fired through a 6.5 mm bore.
Strong rifles protect foolish people sometimes.
The 7X57 is a fine cartridge but it's the bullet that takes the
game animal and the 7X57 is in the same class as the
7mm-08 ctg. Both are fine light rifle cartridges but are not
quite the equal of the longer .270 and .280 rounds. The
short .284 Winchester that was supposed to equal the longer
cased rounds seems to be a forgotten ctg. today while the
7X57 and 7mm-08 remain popular.