I'd first analyze the circuit and definitely leave all the sidechain areas alone. I haven't fully understood how the vca works in the 1960, it's a big potted something, so I'd also be cautious about dc offsets in that area. I'd want to make sure nothing is particuarly adjusted or selected before swapping opamps - unless the service manual with alignment instructions is available? The input / output / micamp / DI in areas should be less critical and might be candidates for swapping. Afaik the 1960 is in fact a fet compressor, so there will most likely be something to align and dc offsets might play a role. Anyway you could mark the origins of the opamps you take out in case something gets weird, but it might also be difficult to hear immediately if something changes for worse.
After 18 years it might also pay off to recap the baby. From my (long ago) experience with other stuff from Drawmer it might also be worth taking a look at the psu and power distribution. And did you ever change the tubes? I just thought about it the other day, mine's still on it's first set of tubes. I never looked into it, it always worked fine. But the standart lifetime of a normal ECCxx might be long over now, I don't know if they had special longlife versions in there?
Replacing the output pots might be a good thing too, in mine they're noisy as hell when being moved.