We are all tempted to do unusual projects or sometimes cut corners to save money on a gun project, but in this case, the words "DON'T DO IT!!!' have special meaning.
Those little Remington Number 4 and Number 6 rifle actions were never designed to contain the pressures and stresses of the .17 rimfire magnum cartridge. Ditto for the Stevens Favorite series.
If you examine the action, you will see that the breech block is simply propped up in place. Strong enough for the .22 Long Rifle cartridge, but certainly not the .22 WRFM or the .17 Hornady rimfire magnum.
Be safe.