A solution for sticky cigar bands
I always remove the band prior to smoking as well as removing the cap. Here is a simple technique to solve the problem:
Holding the cigar between your thumb and fingers, keep slight pressure on the band joint with your thumb. Then, using an Exacto with a curved blade, slice at the joint going top to bottom with blade pressure against your thumb (no, you won't cut yourself), all the while keeping pressure against the cigar with your thumb. This will ensure that if the band is glued to the wrapper you won't tear it.
When you have gotten past the other end of the band, it will release. If the tail of the band is glued to the wrapper, the challenge is to minimize the damage. Cutting backwards, or against the band tail will do the trick. I recommend practicing on "every day" cigars until you have an understanding of this. Then you'll have the confidence to approach all sticks.
When cutting, if you have paper separation in the band, pull it all the way around. This will also reduce the amount of paper you need to release it. Remember, sharp tools do sharp work, so don't be afraid to use the blade between the wrapper and the back of the band.
I've demonstrated this to so many guys, because they are always curious as to how I achieve a successful de-banding, and why I go through the pains I do. My track record is 99.9%. With minimum skill and maximum patience anyone can do it.