Radiation is a safe procedure which has fewer side effects for most people than surgery. Urgency to pee is not a common problem after treatment. Incontinence can be a problem after a few years, but not always.

You should speak to a radiation oncologist, and a urologist who does surgery. Maybe even multiple radiation oncologist to get different opinions.

Have you had a PSMA PET scan to see if the cancer has spread outside the prostate? Urgency to pee could be due to spread.

You have a lot of good options.