Hi Sandy, Drawing 22K or 24K wire really isn't hard to do. And if you have good quality draw plates it's a great way to get any gauge wire at any time you need. I've drawn 22K down to 31 gauge, and going that fine can be a little tricky, but if you take your time, it's not difficult.
Follow Andy C's great advice! It's really important to remember that he says "the taper is only a leader. I get the wire started by pulling on the taper and then re-grip the wire at the meatier place as soon as I can see it."
This is where it will snap off if you don't take care! I use a small needle nose plier to start and then sometimes switch back to my tongs, or just stick with the needle nose.
I also anneal in a small trinket kiln, and keep a close eye on the wire, it will melt easily if you don't. I anneal between every pull after I've gotten to 24 gauge. Use lubrication between each pull as well.
You may want to practice a bit with fine silver before trying 22K.
I know a lot of people think it's a waste of time, but there is something very satisfying about making your own wire, or sheet for that matter.