Let's see how the two cartridges compare in recoil, using Barnes' Cartridges of the World as a data source . . .
A typical 338 Mag load will push a 250 grain bullet at ~2710 ft/sec, using 70 grains of powder. Recoil energy in a 9 lb rifle will be around 36 ft. lbs.
A 7mm STW will push a 175 grain bullet at ~ 3109 ft/sec, using 90 grains of powder. Recoil energy in a 9 lb rifle will be around 33 ft. lbs.
Thanks to the extra powder, you really wouldn't be reducing recoil much with top loads.
You can download the 7mm STW, but you could do the same with the 338.
Suggest you run the numbers yourself and decide if the conversion is worth it.