I think I chose to listen to his story. The Grey Fox gives you the boots back to use for the next quest anyway. Try waiting somewhere in the Imperial City. When I waited for his messenger to tell me where to meet him, I waited in the Market District of the Imperial City (by the crates near Red Diamond Jewelry). I never had to wait long, though. The messenger usually came by around 3am on the day I waited. One day is too long to wait. Three days waiting is ludicrous.
When the next quest does activate, I suggest you not equip the boots near the end. You won't die from the fall. After I used them for the large jump I had to make, I left them unequipped because I wanted to wear boots with better defense. When I didn't die from the fall with regular boots, I reloaded my save and tried it with Jak's boots. Jak's boots were removed from my inventory as I hit the ground. Since I didn't die and my regular boots didn't "break," I reloaded again and kept Jak's boots off. I use them quite a bit when walking outdoors. They're great even if your acrobatics skill is high, but they're much better if it's low.