Which type action for a 7mm? M1891/95 or 98, either is capable of the 7mm round. Makes the decision easier.
FMM or Fusil Mauser Mexicano made a M1910 and the M1934, these are in country builds, not contract. They used the M1912 Steyr due to slow production of the internal factory. There is also a Model 1936/54 or Model 1954, they took the 34 and changed from 7mm to .30-06.
Off the top of my head, there are some South American rifles that are deemed intermediate actions, small rings with 3lugs, basic small version of a K98. Something along the lines of the Yugo Mausers, but its a different variant.