If it has the "walnut shell" stippling, I'd leave it as is, unless you have an exceptionally skilled refinisher.   

If the person restoring it has the skill to shape and finish it to make it like new and it's the smooth stock, maybe.  But, if they just sand it and varnish it like most non-specialist gunsmiths usually do, I'd pass.  It won't look appreciably better and will always look "refinished".

The Anschutz rifles were stocked either in European walnut or beech depending on the vintage. They were then sprayed with a colored lacquer that gave them their brownish-look or in some years, a reddish brown look. Now they're using European walnut and a blonde look by spraying with a clear lacquer. I've seen several that have been refinished and stained to look dark but the stain takes very poorly and leaves a blotchy look especially on those that are stocked in beach. I'd leave it alone like Bob and Steve recommend.

I have restored quite a few Anschutz walnut stocks.  I sand the old varnish down to the wood, seal the grain with orange shellac, build up a marine varnish finish, rub it out, then apply wax.  For the "walnut stippling" I don't sand it, just dimple any areas that are flat and coat it with shoe sole black.  The stocks turn out beautiful.