Great pic of York. A lot can be learned from this photo in re wiping sticks. It's worked for me by tying the string to the patch and feeding down the muzzle with the wiping stick. Give the stick a couple of twists at the breach and on the way up and it usually stays with the stick. If not, just pull the patch out by the string. Oh yeah, make sure the string is long enough so the standing end sticks out of the muzzle enough to give ya purchase to pull it out.
Don't know if York did it this way or not. Maybe he just tied the patch to the stick with the string. Maybe the string acts like the patch itself. Experiment and see what works for you. That's one of the fun things about muzzleloading, everybody has their own way of doing. Key word: "doing". Find what works for you.
Regards,
Johnny