Catching them with the container and then sliding the lid under the gecko to trap it isn't very stressful to the gecko. Just as long as they don't do a lot of running before you cover them with the container.

I wouldn't advise using the wet towel method unless the towels can stay warm for hours. To quickly help her shed lay a wide deep body of water near the basking spot. Soak everything in the tank when you spray and use hot water. Partially cover the screen lid of the tank with cellophane but make sure that the UVB bulbs are under the covering. Leave gaps at both ends of the tank. Your humidity should stay high all day. Buying a room humidifier to increase the humidity level in the room can help a lot too.