Congratulations on being the keeper of such a nice K22. Many people on this board would give an organ to own one in that condition with the box and paperwork. Secondly, kudo's to you for realizing the importance of keeping something that meant that much to you Grandfather. Many people in this day and age wouldn't think twice about the family history of that gun, nor the honor of owning it and passing it down, that speaks volumes about your character. Choose wisely the one you pass it down to, make sure they know and understand what it means.
Thirdly, to your original question, you can' hurt that gun by shooting it, it's already been fired. Shoot it, clean it, care for it and enjoy it. However if it were me, to take the qualification test I would choose the .38. I believe you should qualify with the gun you intend to carry. Training and familiarization is what is needed for profiency with a weapon.
Nothing wrong with using the .22 for your CCW test, just practice with what you will end up carrying.
Thanks for posting those pictures, you have a rare jewel, your Granddad had a good eye for guns.
RD

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Got a Phd from Hard Knocks U