How long haze sticks around depends on a few factors. First, oil based or water based. Oil based tends to linger longer then water does. Second, what is the air flow like in the room in question? If you are moving a lot of air, haze won't linger as long. Poor air flow and haze will stay forever. So if the room has poor air flow, some fans drawing air in and out (like a wind tunnel) would help quite a bit.
As for a good, small hazer, I would recommend water based due to the need to clear the room quickly. The Antari Z-300 II would be a good, inexpensive choice. If more power and DMX control is needed, the Antari X-310 II. I have a few X-310s and love them. Have hazed out large stages running at 10% for hours on end using almost no liquid, or much smaller rooms with the timer keeping it from becoming a soupy mess.
Anymore questions feel free to ask.