This can be a real problem to deal with. Wire snakes are very, to impossible, difficult to use as it can be hard to get them to whatever hole them must get to at the end. I have pulled literally thousands of wires and have tried to do this on my own mizzen mast from only half way up. You may get lucky though and if you lose any of the other wires you might give it a go.
Wire "snot" is a good thing to use. You can find it at any Home Depot or commercial electrical
supply, and online of course.
One of the potential problems can be from how they put the existing wires into the mast in the first place, and whether they used an existing conduit or channel. It seems to make sense to wire tie the new wires in to a neat bundle with a wire tie every so feet, but it can make it a nightmare to get out as the wire ties will snag on things and sometimes will not fit through the holes. I would experiment
and see if only one wire will come up at a time and if so, put a messenger line on it, and use the messenger to pull in new wires. If you can get a messenger (stout cord or a sacrificial wire which is what I like to use) then you can pull out the other wires to make room for the new.
You absolutely will benefit from two people going through all this and unfortunately there will be some time at the top of the mast. It is almost impossible to pull out or in new wires from the top without someone to guy it in. Again, you might get lucky.
The worst thing to happen is to lose all of the existing wires and your messenger (if you get one in) while you are trying to pull the new. The splice between the new and the messenger/old wire is critical. For an easy job it is OK to try with electrical
tape but it should be the best quality tape. And you want to make sure that the ends of the tape will not slough off in holes or whatever as it will jam the wires at that spot. You also want to make sure it is smooth and tapered at both ends of the splice as you may well have to pull it back out before you are successful. It is common to jam a splice, or lose it, when trying to start over.
Electrical wire (I like to use 14 gauge) can be stripped down about a foot and then a loop made at six inches. Then attach the old wires or messenger to that loop with another. If it is small cord you might use a bowline but it has to be small and smoothed over with tape and then covered with wire snot to make it easier to get through holes and tight spots.
Wire pulling is almost an art in itself. It feels good when you get it done. But it can be very frustrating when it doesn't go well. You have to be patient. The wires will always win if you cut corners or get in a hurry and mast pulls are very unforgiving. If one thing doesn't work try something else.
I have sometimes seen where the conduits in masts are not continuous, especially if there were provisions for spreader or steaming lights part way up the mast. They can make using an electricians stiff wire snake almost impossible as there is enough of a bend to make it hard to hit the next part of the channel. And the channel will certainly stop above the step of the mast at the deck and the exit hole can be at the step or it could be up a bit.
Since this can be so hard you want to make each try as likely to succeed as possible. You don't want to have to go up and down the mast more than you have to. And, beware the sharp edges of the holes at the top and bottom of the mast. They can cut a messenger and even wire very easily. I would use a rattail file to ream out the hole a bit if possible, or use some anti-chafe gear
if there isn't any. You should put some in in any case when you are done to keep the wires from getting cut in use.
Good luck and I hope you have a very patient helper as you do this. And compensate them well. I was going to suggest something racy but I won't as it might offend someone on here.