Do you need the slower speeds? Why not shoot for a while and see what happens? I think that Copal has a single crossover at 1/10 to 1/25, or 1/15 to 1/30, so unless you need 1/10 or 1/15 and slower, wait. But if you must....
Take photos as you move along. Especially when you go inside the shutter. I don't remember the specifics of that shutter, but I think it has a part or two that sits on top inside and needs to be, A, not lost, and B, reinstalled properly for things to work. I find having a series of digital images showing the item from various angles again and again lets me go back and find things like how a spring was hooked, etc.
Don't flood the thing. Drip some naphtha into the escapements and work the shutter for a while. If you do apply fresh oil, make certain it is very very light, and is applied very very sparingly.
While the front lens group is removed, clean the front of the rear group through the shutter. Just because...