If you don't have a hot-air gun or something, try putting the PCB in an old pan on some sand and put it on the stove. You don't need paste, just tin the pads on the PCB and put the LED on. But you'd need some extra flux or it'll probably not flow nicely.
Or use an iron? You know, the kind used to flatten clothes. Put it downside up on some fixture, put the PCB on top and heat it up. No idea if that would work, though, normally those irons don't get hot enough before tripping some safety device.