Sorry, I thought you meant the 338 Lapua Magnum as there is a specific 110 made, which differs from the others. Between the 7mmRM & 338 WinMag yes, it’s just a barrel change.

As for a Short Action cartridge in a Long Action sure that will work. The problem is with the Magazines. Just as removable magazines are different between long & short Actions, the same applies to blind mag boxes. A short Action cartridge used in a long or Magnum Action mag box, is prone to failure to feed/jamming with extensive modification to the mag box. Again, the Savage 110 isn’t looked at for a switch barrel Rig except with cartridges in the same family of cartridges.