Some yards like to have the boat on the hard to pull the mast, but I've seen it done in the water without a problem.
The standing rigging can be replaced with the mast up. I replaced a headstay by using a halyard attached to the jib horn and winched it tight. The uppers and lowers could be done similarly. Alternately, the crane can be used to hoist someone in the basket so the mast can stay put. Just remove one stay at a time.