Those are almost certainly fine to use. Glass dielectric parts from Corning are about the most robust caps ever made. The glass body doesn't age, doesn't absorb moisture, and doesn't drift the way ceramics or electrolytics can. The only weak points are the end seals where the leads enter, so look for hairline cracks there or any green crud on the lead wires. If the seals look clean and intact, the guts are basically as good as the day they were made. With just a basic multimeter you can do a decent sanity check. Put it on the ohms range and touch the leads to the cap. You'll see the reading climb as the meter charges the cap through its internal circuit, then it should settle at open or over-limit. Anything that settles at a low resistance reading is leaky and you toss it. If your meter has a capacitance setting, that's a bonus, but a lot of cheap meters struggle to read accurately down at 4700pF, so don't panic if the number looks off by a bit on that range.
As for whether to use them in the rebuild, I'd say use them. A faithful rebuild is the whole point of the project, and an oscillator is exactly the kind of circuit where those parts shine. They have virtually no dielectric absorption, essentially no microphonics, and rock solid temprature behavior. A modern C0G will match them on paper, sure, but it won't match them on sentiment, and the electrical difference in that circuit will be nothing you can measure.
My approach with stuff like this is to use the original parts where they test good and stash a couple in the box as keepsakes. That way the build works and you still have a piece of your uncle's bench sitting in the drawer. Win on both counts.