If you had to do without one or the other in a software project, which would you pick? I've had plenty of projects in which the client or PM thought they could get away without one or the other. We always paid the price.
I'd say you could go without Testing rather than Requirements. If you don't have requirements, how do you know what you're developing?
If the programmers are good enough, they should be able to catch most of the egregious errors that testing would find.