You want the chlorine whatever it is for a standard swimming pool. Should be able to find that on the web. I wouldnt do it right after you shock the pool. I learned this from my canvass guy. A kiddie pool is a great idea.
You will have to work the air bubbles out which makes doing it in a garbage can kind of difficult. Try and "feed" the cover into the water to avoid trapping air.
Last time I re-waterproofed my cover I used Starbrights product in a garden pump style sprayer. I was very happy with the results and its much less expensive than 303.