What would you do if the crap emergency was this big ?

Probably the same, unless there was a container around and using it was a viable option. Like if you're driving and traffic is crawling but not stopped, it would be difficult. Or if there's more in you than what the container can hold, it could be worse of a mess. Anyway, if it was an emergency, I think you did the right thing by going in your pants a little as you did.