There are several points you can make to a reluctant GP
1. The option of not having a catheter is "involuntary urine retention". Medics take retention seriously (it qualifies as an emergency).
2. that the autonomic nervous system's reaction to a threat is retention - it closes the urethral sphincter and relaxes the detrusor - so however much you want to pee, the body wont let you, even if bursting.
3. Hospital training makes medics wary of catheters due to the high rate of infection there. but outside hospitals, our experience of male self-catheterisation is that infection is almost non-existent.
4. you are hopefully not going to use them every time, but only intermittently when trapped. Also having one available will reduce your anxiety so much that you may feel be able to pee in a cubicle normally.
5. an article in a nursing trade magazine surveyed self-catheterisation and recommended its use for self-management. I can provide the article if you need it.