First thing to do is get all of your tools and supplies ready! Flat bottle opener, clothes hanger, container to hold liquid, bowl to rinse coil, toothpick, screwdriver, screw clamp.
Use a flat bottle opener so that you don't bend the cap out of shape
Lift edge slightly, then turn globe. I turned it less that 1/8th of a turn each time.
It won't take long before the cap is loose enough to remove and it can be reused.
I drained (and saved) the liquid to make working with the coil easier
Now to remove the coil. I used a wire clothes hanger to snag the coil, any stiff wire with a small hook will work. Since the coil was easy to get to, I didn't have to melt the wax.
A little bit of junk stuck to the top of the globe, I cleaned it before continuing with the coil.
I cleaned the gunk off of the coil, then rinsed the coil in hot water. I continued cleaning with a toothpick to remove all of the gunk. Sadly, no wax was able to be saved. And FYI, the coil has an adhesive holding it together, I found this out after I had cleaned it off and the coil came apart. But by pressing the coil ends together it holds together just fine.
Then I refilled the globe with the saved liquid
and then replaced the coil
Now to replace the cap. Put the cap in position and place screw clamp around it.
I held the clamp centered on the cap ant tightened. Then I placed the clamp lower around the crimped edges and tightened again. Then because the clamp left a small pinched area, I loosened the clamp and turned it about 1/3rd, tightened again, and repeated. Whether I needed to do all that or not, it worked.
Globe on the right. It is not as yellow as the picture shows, it's more of a cream color. The cap has rust on it so I will need to find some bottle caps and redo it, maybe add color to the water also.