If memory serves the old sails were treated with a broom, acting as teh paint brush. So the sweeps could be quiet wide. And from a recent post, the bolt ropes woud also get treated att eh same time by default.
It should be possible to carfullly mask the mast and deck, and then treat teh sails with a tooth brush.
For Dye.
For cotton, there is Dylon cold water cotton dye, wich comes with a fixer. You could brush on the dye with said toothbrush and, when dry, brush on the fixer.
Dylon also do a dye for synthetics, but this i think is warm wash. you need to check.
For synthetic Nylon sails (Don't know about Dacron) one of the members on here (Romainpek) succesfully dyed sails using a water down acrylic paint.