So how should I go about removing the wick so I can dry fire it and check to see how it's lights up?
You don't need to remove the wick. You need to use a syringe, and remove the juice from the tank. Then, with the mod horizontal, keep dry firing in short bursts, until you see the coil begin to glow. When the wick is dry, you'll be able to see whether or not your coil is glowing evenly. If it isn't glowing evenly, you can gently bump the wires around, and work out the hot spots.