You don't want to remove all the ammonia from your tank, no ammonia means nothing to change in nitrItes right? Instead bring it down to a safer level, which 0.25 ppl should be fine. Anything over 1ppm is hard on fish. No idea on the guppie though, personally I'd take it out and treat it and leave the other two to cycle the tank.
Also if you can find someone with a cycled tank, you could snag a bit of filter media or rocks to put in your tank to jump start the cycle. Keep them wet with tank water of course and get into your tank ASAP. This is how I start a new tank at homes, I have panty hose with rocks sitting at the bottom of my big tank and extra sponge in my filter. I just plunk some sponge in my new tanks filter, put the gravel in and in a few days, cycled.