For what it's worth:
I heartily agree with those who suggest messenger or mouse lines. If the cord is light, it's a good idea to 'tack' them to the mast
with a really durable tape to prevent them thrumming - just needs a 50x50 square patch every 3m or so... you can cut a strip of the tape and stick it (reversed) up the middle of the sticky side of each patch, so pulling the messenger through is not a major struggle.
The best idea for leading end of the halyard
which is to be rove is a "Flemish eye", to which you can hitch, using half a simple sheet bend, with the messenger end. This renders nicely through the boxes and round the sheaves.
When this gets to each square of tape it peels or bulldozes it out of the way. If any patches remain stuck to the halyard
, you'll need to bring it back down and remove them before they reach the halyard box.