The problem you'll run into doing this is that the 243 will have a push feed bolthead with a plunger type ejector located in the bolthead. The WSM needs a control round feed bolthead which has a mechanical type ejector which is located in the back left of the action, it doesn't exist on a push feed action.
This can however be overcome, sorta, you can switch to a long action magnum bolthead for a push feed action and it will function fine for a single shot WSM, feeding from the mag however will ah.....leave a lot to be desired if it works at all.
If you go the single shot route you will still need a little work done on the bolthead. On the back of the short action bolthead there is a small indentation that is not present on the long action bolthead, you'll need to have one machined into it. Last one I had done cost me $50 including the long action bolthead.
Hope this helped.
Ignorance can be treated with education, sadly there is no cure for stupidity.