Bravo, great gun, great friend!
Made from 1994 to 2009. For your records if you want, it's a:
MODEL #06511
CATALOG #SSM-4F-S-I
SSM = Single Six Magnum
4F = 4 5/8" barrel Fixed sight
S = Short grip
I = Ivory (simulated)
Yes, you can put any Ruger grip frame on it that you prefer.
The next size up is the XR3 size, standard length with 1/8" less space behind the trigger guard and 7/16" thick for a slimmer feel. This is the same size as your old model 357 if it's a flat top made before 1962.
Early versions of this grip frame came with the internal lock. It will work fine on your gun whether or not you want to use the lock. If you get one of these get the lock with it, but these can usually be found cheaper than w/o the lock. Or bypass and don't use the lock. Just ask if you want to know how to bypass lock.
Then the XR3-RED size standard length and same space behind the trigger guard and 1/2" thickness, same as your short grip, (this is the grip that came on this model with the standard grip size). This is the same grip size used on your old model 357 if made after 1962 and with the rear sight protective ribs.
Both available in blued steel or stainless. You can use all of your parts; screws, mainspring & strut, trigger spring, and all the pins.
If you get a new grip frame it'll be oversized and must be filed and fitted, polished, and blued (unless you use stainless of course). Look for a nice used one $100 to $120. But fully finished and fitted. It may not fit exactly but usually from very good to perfect.
Comparison of grip sizes for your reference (shorty not shown):