Recoil calculator will tell a lot.
The numbers don't lie, a 243 is probably ur best option with no brake. It will absolutely no be too much recoil. A 6.5 might tho
Assuming 7.5 pound rifles the 140's from 7.5 rifle should giv u about 13 ft lbs free recoil energy vs ur 7mm's 23 or so..
Now this is where it gets "fun"
A 243 would top out at about 10flt lbs with a 105 but an 85gr bullet at
3000 fps would be down to 7 or so. H4896 would offer even lower loads
Or brake any other 308 base round with 120 to 140 grain bullet. And be down to that 6 to 8 range.
Ultimately its a coin flip but I think brake is a better long term option. Muzzlebrakesandmore or lil Basra d should reduce 13 lbs recoil to about 6 and ur placing less demands on the bullet to function properly.
Or last option is spin up so 120gr ballistic tips over a light charge and brake the gun and u can avoid a whole bunch of hassle with buying a new gun.
125gr over 55grains in a tikka super light 300 with a brake was probably was easier on the pad then an over gassed m4gery with 75 bullets