credx, refinishing the stock will only improve the value of the rifle, I doubt at this point "used but original finish" makes a difference, this is not antique furniture.
I disagree so with your described method of repair, from what you say about "finish flaking off" the stock is varnished, not oiled. Once you start going at it with wax or oil, it's going to get worse and you can't fix the varnish anymore. Remove an damaged varnish with the fine steel wool, roughen up the rest and recoat with shellac or similar. Or sand it down and give it an oil or wax finish.
F 135 - the right choice