It would probably drop a little less than a pound, maybe 3/4's. I swapped out the wood for synthetics on my pardner 12 and there was a noticible difference in weight, but on the scale it was less than a pound.
Edit: And most of the weight loss is on the back half of the rifle, the butt stock area. I don't know how much this will help him hold it steady since it will probably be more barrel heavy with the lighter synthetic stocks.
One thing i'd also consider before dropping nearly a pound off a 243 is recoil. A 6 3/4 pound 243 will kick harder than a 7 1/2 pound 243.
If the shooting sticks are hard for him to control you might want to look into a harris bipod with swivel base (swivel is a must for uneven ground!). If you get the harris S-25 the three piece legs will extend from 11" - 25" which he can use for prone, sitting, and kneeling. Just another idea.
Hope this helps.
later,
scruffy