Around here a good price to unstep the mast is $6 a foot of mast (30').
The problem is the boat is already out of the water. The boatyard probably can't unstep the mast using their normal procedure. I don't know how much you would save paying to splash the boat, then paying another boatyard to unstep the mast and haul the boat again.
To do it yourself you have to rig something higher than the spreaders to lift the mast straight up a bit--like that ladder. I've also seen pictures of A-frame arrangements.
The mast only weighs about 80 lbs., but its clumsy. The real danger is somebody taking a header off the boat to the pavement below. Not good.
Here's a pic of the bottom of the mast. Those two "keys" fit into the slot of the mast step.