If you do a 100% water change, that's just fine. So long as your new water closely matches the old water. In temp, pH, etc. If one or more of these parameters are too different, this could cause your fish a great deal of stress, and kill some of them. Since the beneficial bacteria do not live in the water, but on the surfaces, there really is no danger of a cycle or anything other than the potentail disaster that can occure if the new water is drastically different from the old water. It is key to change water that closely matches your current water. I also think it is key to find out what is causing the cloudyness. Algea? Unrinsed gravel? Bacterial bloom? Something in the air somehow affecting water? Once you narrow down why you can start coming up with other possible solutions.
When I changed gravel in my two tanks, I had no mini-cycle of any kind. In both tanks (a 20 long and a 20 high) I also did a 50% water change. It was a quick process (about 2 hours total) and I had no fish losses/illnesses and again, no cycle. I saved 1/2 my wter in buckets, but plants, and decorations in one and fish and floated a few plants in another. I removed all gravel, cleaned my glass with a wet sponge (for tank use only, no detergents/soaps ever) then added my sand. Added my new water (pre aged to match pH and temp of old water) added my plants and other decor then added my fish. I personally felt it was much less stress on my fish to have them in full bucket(s depending on number of fish) than having them in low water with my digging and rearranging everything while they are in the tank. My water was a tad cloudy for about 5 hours, fish were fine and happy, ammonia/nitrites tested daily for 2 weeks, with no measurable raise in either.
As far as starting gravel vac, it isn't unsanitary if you get some tank water in your mouth. Just won't taste so good. I don't think you will find a documented case of a fishkeeper getting ill from ingesting a few sips of tank water. I personally don't like the taste of tank water, so I use the "shake" method Teelie mentioned.
\Dan