I found a trick that makes fletch tape an absolute pleasure, although that video is a great idea also.
I found that using a very small set of spring-loaded dikes/wire cutters are the best tool. After you apply the tape to the feather, you can trim the ends with the dikes. If you apply light pressure, you will feel the dikes actually pop through the tape portion, but will not cut through the plastic tape backing. It's great. You can snip the tape on any angle (to match the front end portion of the feather), then, keeping the dikes closed, just turn the dikes toward the feather and pull, and it will remove the backing (since it only cut through the tape, and not the backing). After a few tries, you get the feel for how much pressure you can use, and you're all set.