I met a family at the range one day that had cut down their rifle's stock to short enough for their youngest kid. They bought a universal plastic butt plate from Brownell's and ground it to fit. As kiddo grew, the thin plastic was replaced with successively thicker recoil pads. When the rifle was too short for the kid, he receive a new rifle and the cut down rifle, complete with its set of recoil pads, was passed along within the family. I had the pleasure of meeting boys seven and eight years old, the fourth generation.
The stocks of most .22s taper to the butt. The original butt plate will not cover the cut. It is best to makes some measurements and get the Brownell's plate before making the cut.
Take a good look at lace on cheek pieces. Small faces must get up off most stocks to align an eye with irons sights, even higher off the stock for a scope. A "cheek weld" is a real part of marksmanship.
If you have a 'smith do the initial cut, make sure he understands that the cut is to get the correct length of pull with the thin plastic butt plate. The 'smith my friend entrusted the honorary nephew's Savage MkII to did not have the thin plate, so he cut for a 1½" recoil pad, leaving no chance for the stepwise increase offered by successively thicker pads. The Boyd's replacement stock, bought when kiddo grew, cost about 60% of what I paid for the rifle. While poor communication and incompetence are the probable causes of the problem, not fraud, I feel ripped off.