My hen's lump was big enough that I could cut a small slice (just one, not an X) right across the top of the lump. She started bleeding so I soaked her and then I was able to see the yellow plug. Rather than poke around with the knife, I reached in with my nail and scooped it out. That's why I'm not sure I got all of it; would have been easier if I had help.
If your lump is smaller than a pea, unless you can see a yellowish spot on the lump, maybe just try to keep soaking. Could just be infection from the thorn and maybe that will cure it
Your list of on-hand items is pretty much all I used except instead of rags I used paper towels. I also placed a gauze pad over the wounds before taping up. Not sure if that was necessary but it made me feel better.
If your lump is smaller than a pea, unless you can see a yellowish spot on the lump, maybe just try to keep soaking. Could just be infection from the thorn and maybe that will cure it

Your list of on-hand items is pretty much all I used except instead of rags I used paper towels. I also placed a gauze pad over the wounds before taping up. Not sure if that was necessary but it made me feel better.