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I think it all depends on the upgrade.
Silk/Magic sails could be swapped out in a few minutes if you get your whole crew to put their backs into it.
A broad rudder would probably take a few hours to install on an average sized sailing ship and wouldn't necessarily need to be done in a dry dock.
Smuggling compartments would vary time-wise but would be unlikely to require a dry dock.
Ram and Glass Bottom installation would almost certainly require a dry dock, unless you think cutting holes in your hull while the ship's in the water will work for you.
etc.
As far as how long it takes, consider how many people are likely to be working on it, what the modification is, how long of a line there is, and how much you are paying.
There's nothing concrete listed in the Player's Guide about time constraints on ship modifications. You could probably reverse-engineer it using the craft skill rules, but that's going to be a pain in the neck and probably result in something completely bananas.
You might have luck bribing the management of the shipyard, or at least a medium-level supervisor. I imagine that greasing the right person would or could get you bumped up in line (at least a few places) if you're in a hurry.
A thrifty Rogue with ranks in Linguistics could conceivably sneak into the office after hours and change/forge the work schedule if you don't like paying bribes.