My husband was born with hypospadias where the urethral opening is all the way at the base of the penis or on the shaft. He had numerous surgeries as a child to fix it to some extent, but because it was severe, the opening is still on the upper portion of the shaft. The only problems he has are cosmetic. Oh, and he has to be careful when he urinates standing up.
I completely understand wanting to correct your penis for cosmetic reasons. My husband looked into for a long time before deciding that none of the surgical options would work well for him. I know he'd like to have a more normal-looking penis, but I know he's pretty much accepted himself the way he is. We have a perfectly normal sex life and were able to have a child with no medical intervention.
Though the skin you may be grafting on is sensitive, any scar tissue that develops will not be as sensitive as what it was before the surgery. If what you say about the doctors is correct, there is a chance that you can have more sensitivity, but for the most part, any surgical procedure results in decreased sensitivity where the surgery was performed. I'm not a surgeon, but this has been my experience personally. Surgeons like to sell their procedures the same way any other businessperson does. I would want to speak to others that he's operated on. I know my orthopedist told me that my knee he reconstructed would be perfectly normal and my scar would go away. 15 years later, I still have trouble with my knees, my scar is stil there, and I have little sensitivity where that surgery was performed and in the area around it. My more recent c-section scar is the same. I just can't see how you would get more sensitivity with further surgery. It sounds like a long shot.
I suspect something similar with the cosmetic aspect. From what my husband has had done, the reconstructed skin does not look like regular smooth penis skin. There's a good deal of scar tissue and you can tell where the grafts were done. In his case, surgery was necessary because of the severity. However, further surgery would cause even more problems that I don't know would solve much except maybe put the hold further up-- but it still wouldn't look normal. And it wouldn't work any better, and could work worse.
If my son had been born with mild to moderate hypospadias, I would probably not choose to correct it based on my husband's experience. I think as long as the penis is functional, it's probably a good idea to just leave it alone.
Finally, you have absolutely no reason to be embarrassed about your penis. None. It's nothing that you did to yourself and any man or woman that can't accept you the way you are isn't worth it. I know how hard it is to accept that, but you truly have nothing to be embarrassed about.
Take care and good luck. If you do choose to have the surgery, good luck and please let us know how it goes.