"Barricade" formerly "Sheath" works as well as anything else. Regardless of which gun oil used this nice old Colt needs to be oiled up. Just keep oiling it and the rust will eventually disappear.
Be careful he doesn't recommend that they do their "This Week $199 REBLUE SPECIAL!" Many gun shops don't know collectibles...they know black plastic. I've even had pretty good gunshop "smiths" jimmy up a screw on the hammer of my Trapdoor Springfield, another "polished up" an nicely patina's piece of 1860s brass. Be careful, that gun is worth a couple grand at least. Many a $5,000 gun has been reduced to a $2500 gun in 10 minutes of unknowledgeable cleaning. Even by "gunsmiths". Personally, I wouldn't let a local one touch that gun. Unless you know they are good.Thats for all the advice and comments everyone. I live in Washington state and the gunsmith is closed due to the coronavirus. Once he opens up again I will take my gun in to him to get the latch fixed and see if there is anything he recommends to get it all in top notch shape.
DO NOT SEND IT TO COLT!! It will be returned. They have not worked on those guns in well over 30 years.Bran357 - that is a valuable and rare Colt. Find an experienced Colt gunsmith (or maybe send to Colt?? I don't know Colt's situation these days). I suggest you also consider purchasing a Colt factory letter ($75.00?).
Getting out into the "weeds" a bit:
I purchased a factory letter on a Colt 1903 in 32acp; the pistol was a WWII bring-back from the Pacific Theatre. The Colt letter stated the pistol was sent to the Dutch East Indies National Police Force in May 1941. When the Japanese over-ran the West Indies (now Indonesia) a Japanese office took possession (officers were allowed to have other-than-Japanese side arms). A GI stationed in the Pacific brought the gun back with him (I have a copy of the US transfer paperwork).
Point being: a Colt factory letter on your gramp's Shooting Master 357 would be interesting + add value IMHO.