Well it's done. I used a seam ripper and a small pair of scissors. The only hard part was removing the stitches near the seams of the knickers, since I was concerned that I would accidentally cause a hole in the seams. But it looks like it worked out okay. You can still see the tiny needle holes forming a zigzag pattern in the shape of the chamois, but I'm hoping they close up over time.

And now I can wear the knickers for cycling (over padded shorts) or in place of sweat pants for taking walks, going to/from the gym, etc.