I want to remove a darkish (but not deep) woodstain from a kitchen dresser without using miles of sandpaper. It clogs up very quickly and I wondered if there was a cleaning agent that would do the trick?

Stains are as the name implies. A stain. It goes into the wood. Paint is a surface agent. Rule of thumb, you can restain darker NOT lighter. I think your plan in near impossible. Give some thought to reveneer and restain. Call a custom cabinet person. And at that putting on a stain can be an adventure if the cabinet shop doesn't have the right equipment