Whatever you do, and in my opinion Patchworm is the best, do NOT use a pull through made for firearms and which has a brass bristle section. It will thoroughly chew up the O-rings in the barrel and transfer port section.
I have been making my own pull-throughs for the last 5 years. Just a 3 ft length of weed whacker line with a copper single hole crimp on the end. They work great & the cheap roll of weed whacker line will last longer than I will. Just recently I added a nylon bushing in front of the copper crimp. Never had one break, never had a crimp come off.
I've been using a "Crown Saver" pull through with patches for many years... have a couple extra in case I wear my original one out, but it's still good... I don't need to use it too often since I lube my pellets... only when I think the accuracy is off.
On using the fire arms pull through , I just take the bristle brush out and leave it out. Very simple to do . Then I just use that pull only on my air stuff.
I use a piece of heavy weed wacker lime and heat on end and push it into an empty 22 rimfire shell to expand the end. Then sharpen the other end of the line. Then I bought a bag of assorted soft plastic caps used to block different sized automotive vacuum lines from the auto parts store. You just slide a patch down the line to the bump on the end for a 22 cal. You can use the plastic caps to use with different cal. I use mine fore everything up to 50cal. I also use it on my powder burners. You just poke a hole in the caps and can piggy back the bigger ones over the smaller ones for the bigger cal. to make a tighter fit instead of having to add multiple layers of patches.