Here is a method I've had good luck with when I have to repack a tip cleaner.
First, visit a hardware store, not a big box store but a real hardware store. Ask if they have any graphite valve packing. Look through all the various sizes and make note of any broken ones. The ones in the photo below are about 1 inch in diameter and a half inch wide by about a 1/16 inch thick. After lamenting that you can't find the size you need, pick up a few of the broken ones and ask "What are you going to do with these broken ones?". Most likely they'll say they're going to throw them out. "Can I have them?" is your next question. Armed with your supply of packing material, head for the workshop.
Cut some small slices from one of the broken pieces
Don't worry about how neat or how big the pieces are as long as they're small enough to fit in the space between the cleaner wire and the nut.
Here's the cleaner clamped in a small vice, the sleeve and nut held up out of the way with a small piece of wire. Pack the pieces of packing you've cut around the wire. Don't worry about neat, just pack as much as you can in the space.
Here's how it looks after you've stuffed the thing full. Now, using a piece of stiff wire or rod that is small enough to fit between the cleaner wire and nut, and a small hammer tap the pieces down into the nut. I made a tool to pack the nut out of a piece of coat hanger wire hammered flat and filed to width.
Once you've tapped the pieces down, slide the sleeve and outer nut into place and tighten down the outer nut.
Crank it down tight, but be careful, you can tighten it enough to torque the inner nut in two.
Open it up and take a look.
You should be good to go now. If not add a few more pieces of packing, tamp them down and go again.
I've used this same method to pack a fuel valve. It's easier to buy a packing from Mike at OCP, but if you're all out and need to get a lantern going this will work.
North West Florida
Reese’s Law of Thermodynamics: At temperatures below incandescence hot metal looks exactly like cold metal.