Here is an optician nose pad removal tool that is designed like the nose pad popper ( a tweezers version of the same). This tool as well as the other mentioned nose pad removal tool is shaped with a two prong end that braces the nose pad arm while pushing the hard base of the nose pad through it to easily snap it out. You can see this from the images. This particular nose pad removal tool is a high quality tool that has a built in spring tension system that keeps the tool in an open position. This allows you to squeeze the tool (when in place) to easily pop the nose pad out of the metal nose pad arm.
Please look at the images to grasp the idea of using this tool, as well as checking the listing for the nose pad popper.