According to the FDA, cyanuric acid by itself is basically non-toxic. It is used in some places to disinfect drinking water, too, so I wouldn't worry about it in a properly maintained pool. It is not metabolized by the body and passes out through the urine.

Just don't drink that pool water along with food illegally spiked with high levels of melamine, like those bad batches of Chinese pet food and infant formula from a few years back. Combine the two and they precipitate into crystals in the kidneys and lead to kidney failure. Actually, the pool test kit for cyanuric acid does just that--contains melamine and you gauge the level of cyanuric acid by observing how turbid the water gets when they mix together.

When I thought about it, by not using a stabilizer, isn't it going to be difficult to maintain the proper concentration of chlorine in your pool because UV from the sun decomposes the chlorine so quickly? It seems like you would have a safer, cheaper and more convenient to maintain pool if you use the cyanuric acid.