Yes, there are various type of urethroplasties the one you suggest being one of them. I’m curious why the doctor didn’t recommend one of these procedures. Possibly because Catheterization is the simplest and least invasive. However catheters do carry serious risks. My Dad developed bladder cancer from chronic catheter use along with infections. I’d be curious about the statistical data regarding bladder irritation and cancer.
There are risks regardless of the choice you ultimately decide on.