No real answer, but I did want to let you know that I made the mistake of letting my son just splash a bit in our kiddie pool last summer, in water that had been in it for 4 days (like you said...just about the time it finally got warm!!!). Anyway, I knew I was pushing it, since the water was starting to get a little cloudy, but I thought, "I'll just empty & clean the pool right after he's done playing in it", which I did. Big mistake by letting him play in it at all. Several weeks later, I ended up having to take my son to the doctor, who then referred him to a dermatologist, because he got a funky skin rash (foliculitis) that had to be cured by $125 special RX foam.
My advice is to empty the pool daily. Scrub it out as well (use bleach). When it comes time to fill it, hook your hose up to an indoor faucet where you can fill the pool w/warm water. Trust me, this all will be worth it. You do not want to go thru what I went thru trying to clear up my son's rash. It took 2 regular doctor's visits, one specialists visit, and a total of 3 different scripts before the dermatologist finally got it right (he got it right on the first visit).
Hope that helps. Oh...this year, I'm buying a pool that is a little bigger, but has an electronic filter AND can accept chemicals. No more funky water for me!