As Neil says, the only way to fully treat urine in mattresses is with a syringe. You can clean the surface in the normal way. As long as you let the customer know exactly what you can and can't do, it should be fine as long as you get the job done properly.
I always advise them that the mattress will be out of action for at least 24 hours, maybe 48 hours to be on the safe side. I mix up a jug of my solution and literally just keep refilling a syringe and work in a grid pattern, about 2 inches between injection points. If the visible affected area is 1ft in diameter treat an area 2ft in diameter, as it can wick along under the surface without being seen.
Because you're working blind you can't see if what you're doing is enough to cover the problem, so you really have to go overboard just to be on the safe side. I have injected over 2 litres of solution into a mattress before.