How long does nose skin take to regrow?

The procedure you describe is necessary from time to time particularly for a condition called rhinophyma. The time it takes to heal depend on how deep the skin is scraped. Anticipate a week to ten days to heal but it will be red for several weeks after that

How long does it take for a scrape of the nose to heal? How long it takes a scrape to heal depends on the depth of the injury. A scrape which is not deep enough to cause bleeding is probably superficial and will probably heal within 7 to 10 days. A deeper scrape will take longer and a very deep scrape may leave a scar.

If you cut through the dermal layer of the skin, whether it's a scrape, a shave, or a laceration, it will always leave a permanent scar. The only question is how visible the scar will be. Some of that depends on your own biology, how you take care of the wound (sunblock, silicone gel), and what the type of injury was and how big the original wound was. So yes it will grow in and heal, but it will never look the same again, unfortunately. You can use other modalities, such as laser or other treatments, to minimize the scar long term. Good luck!