No, it's OK to the have a higher voltage rating, too.
However, if you go too far up in either or both, you'll eventually find that you've got a big-ass diode that may not fit in the space on the PCB.
Be careful applying this information... as it only applies to "regular" diodes. "Zener" diodes are quite different, and their voltage must be matched closely, because of the different way they work and are used.
I checked Radio Shack, and didn't see anything they typically stock with the specs you're looking for. If you want to live on the edge a little, I'd say try a 3A 400V diode, like a 1N5404. Radio Shack carries them (P/N 276-1144). My reasoning: IMHO it's pretty likely that the thing pulls more then 1A on the 120VAC line, esp at start-up. As a result, I don't think it's wise to skimp on the current rating and use a 1A diode. The voltage on the other hand, appears to have some safety factor. The peak inverse volage that is likely to appear across the diode is 2X the peak line voltage, or about 340V. SO, a 400V diode should be fine, just with less over-design/safety-factor. It probably won't last as long as a 600V rated diode, nor handle as much abuse due to a surge etc.... but it should work fine.