A 115-grain .243" bullet would help a bit, but you'd never get the same velocity with the .243WSSM, so performance would be lower. The difference in diameter is just 0.014", but the 25wssm has 13% more area for the propellant gas to push against, giving higher velocity. IMO any real advantage for the .243/115 load would be in extreme-range target shooting, not on game. If you need a heavier bullet, get the proven .25wssm.
The .243" is simply a more popular caliber than the .257". The .257s were highly popular until the introduction of the 6mms in 1955, when their popularity began to fade. BTW, the old 6mm Lee Navy cartridge (ca. 1895) used a 112-grain bullet.