Some vets don't use anesthetic, or use agents that paralyze the muscles to prevent movements, but do not use any analgesic. It just seems cruel to me when a local anesthetic like lidocaine is about one cent per mL. I know for a while in horse castrations, vets were using succinyl choline, which is a muscle paralyzer, but does nothing to alleviate pain. This is now considered inhumane and vets could lose their licenses for doing it, yet some still use it in their practices. I'm certainly not criticizing your vet, but my personal feelings on the subject is that I want to use some sort of anesthetic (yay for local anesthetic!) in any procedure I do. We've been using Lidocaine in many of the recent large animal procedures I've done.
If you have a good understanding of antibiotics, it is do-able, but not advisable. The problem is that if the blockage is further up the urethra, like say in the twisty sigmoid flexure, cutting off the tip of the peni.s can cause more issues than it may help. Additionally, giving an NSAID and performing a "surgery" on an animal can cause all sorts of other issues.
I definitely understand having to resort to home remedies when you don't have access to a vet. It just makes me cringe because I've seen so many animals come into the clinic with issues that well-meaning owners tried to fix. Then these animals have not only a primary issue, but also a secondary issue that can complicate things.
ETA: I am looking up the procedure now to see what the steps are just in case I am off in the procedure I am thinking about.
ETA#2: I looked up the procedure and it looks like the two most common methods of anesthesia in these guys for this is diazepam (valium - works as a sedative) or epidural anesthetic. It looks like you could also use general anesthesia as well, but it's not a terribly difficult procedure. I don't know if anyone is interested, but here is a nice paper about the procedures.
http://c.ymcdn.com/sites/www.michvma.org/resource/resmgr/mvc_proceedings_2014/holcombe.pdf