My process may require more than anyone wants to deal with, but...
I use the corkscrew style pin pusher. I start with the short push pin since it is stronger and more stable to push the link pin out of its "groove." I push as far as the short pin will go. Then I back out the whole pusher, remove the short pin, install a long pin, and drive the link pin as far as that push pin will move it. From there I can usually just pull it out with my finger, but if needed I'll grab it with a pair of needle-nose pliers. You do need to take care that everything is lined up just right, and that your bracelet doesn't start to wander off at an angle. Otherwise, the pin pusher will snap. That's why I have extras!
I'll screenshot a picture of the tool I use, and link the website of the store I got it from (kinda like a West Coast Esslinger). It even has a hollow area if you use a blade to pry open the bottom plate. That's where I keep my spare pins!
Watch parts & supplies, http://www.ofrei.com The finest watchmakers screwdrivers available in the world are available from Otto Frei www.ofrei.com<br> Around the world, the Swiss made Bergeon Watchmakers Screwdrivers have long been considered the best and highest quality available to both...
www.ofrei.com
(yes, the website is ancient but it still works)