Considering the male stigma regarding the removal of the testicles, are female urologists more suitable in performing bilateral orchiectomy?

If there is medical indication for orchiectomy, it would not matter if your urologist is male or female.

You are presuming 'stigma'. If medically necessary Urologist of any sex will do the procedure

The gender of the physician performing a surgery does not matter. You should see a doctor whom you feel comfortable with. If you feel more comfortable with a doctor of either gender, it is your prerogative to seek that physician. Good luck.