a .243 Win is a necked down .308 Win. The .243 WSSM is a completely different case. It has a much larger diameter body and rim, which increases case capacity. I do not know if the 788 can be modified to accept the "magnum" dimension WSSM rim. If the bolt face can do it, then you have to consider feeding as well. The WSSM will almost certainly require modifications to the feed ramp, follower, guides etc.
Lastly, and someone who knows beter should jump in if I am wrong, the 788 was not known as the strongest action, and the .243 and .308 versions have been known to suffer from "setback" due to the recoil lugs weakness. I read about this a LONG time ago, so I might not be remembering it correctly. Why don't you just sell the 788 and buy a low end WSSM? It would probably not cost more than the work on your 788.