first of all, choose well your pee buddy. I chose a male friend I have a lot confidence with. I can say I love him as a friend, and I think he cares quite a lot for me. He is not paruretic but I knew he is very empathic with me. I think a non-paruretic friend may be even better than a paruretic one.
I had planned a holiday with my family and his, so I took the opportunity to tell him that maybe he could help me if we had to pee together in the open air, or in the public toilet. He promptly accepted. Actually, I had already desensitized me with "street urinals" and also in urinals with dividers. My difficulty was in urinals without dividers and in troff urinals (that are not used in Italy). My friend and I have practised every day at least once in the "open" urinals we found in restaurants, pubs, visitor centers and so on all throughout Ireland. I did not know, but troff urinals are quite common in Ireland, even troffs where you urinate against a "wall" and then your urine drains downwards in a groove just in front of your tip toes. These were very difficult in my mind. I must say that my friend's presence was very reassuring and I could urinate almost in every situation and in any type of urinals. Sometimes I have also practised alone, usually successfully.
I think it is a good idea to propose to your friend to enter the cubicle with you first, or also in your house, then to keep open the door, and then to try the urinals (possibly with dividers first). When you try the urinals, initially let a urinal free between you (usually another man will not use it due to "urinal etiquette" unless the toilet is very crowded), and then put yourself in to two close urinals. In troff urinals, I advise you to put yourself in the corner and your friend as close to you as you are confortable. Try talking with him while trying urinating, it is relaxing, and you will feel more at ease.
Good work, and I hope you fill find a pee buddy as good as mine.
If I can be of help to you again, write me again!
Nick (from Italy)