just put a pump in it. It will pass a smoke test with a bad pump. I would spend some $ on a pump before spending $100 for somebody to tell you it needs a pump.
Most of the time I don't use the valve. I just pump it from fuel cap. Its faster to set up. In your situation, I just replace the pump and not worry about a smoke test. I'd it was a 442,455, or 456, then I would smoke test it