Kerethos said:
Male or female, I don't see this scenario being very enjoyable. You'll either be a sperm factory (as insemination is a fuck lot more efficient than intercourse) or a constant baby oven. Either way sex won't be on the table. Getting strapped down and used is what you're in for.
You'd have to be damn quick to kill or castrate yourself in order to escape, because once you're in custody you'd be under suicide watch or just permanently kept in a coma (to ensure you don't hurt yourself and can be monitored at all time).
Nah, nothing so dramatic is needed.
The first priority would be simply stay out of sight and then put on a burka or a nikaab or some such, as nobody is expecting to find a guy anywhere anyway and then just look around first.
Then you'd soon figure out that the limiting bottleneck is not your balls, but the tiny capacity of already closed-down IVF clinics and the lack of specialists, as the catastrophe had come unexpected.
Once you get found out, out of a 7 billion total of dead males and living females and grannies, only about one billion healthy young women might be eligible for IVF treatment and the waiting lists would be decades long.
Production on your end would become a trivial matter after a short while, as there's easily a billion spermatozoids in just one spew, if you're a healthy guy.
If the system were globally and efficiently organized, you'd have an initial rush of tiny, cooled drops send to clinics across the globe. If not, then just one small beaker to the one lucky, local clinic in the region where you were dropped. That might be inconvenient, but then it just becomes infrequent.
OP's fantasy of becoming a highly prized, recreational, sex slave is actually more plausible than milking it for the rest of your live, like it were actually milk for drinking.
Same for the female version, because there would be no hope for the world anyway, so no need to even bother with the baby oven idea.