You won't damage the liner with the bleach. After you add it, take a broom or oar or something and stir it around to mix it in. Can you hang the cya sock in front of the hose? If it is going to take 4 days to fill, you're probably gonna have to test and add bleach a couple of times a day --- morning and evening since you have no cya in there yet. (and, if you are home this weekend, maybe even in the afternoon.) Go ahead and get the bleach in there. It doesn't take long for algae to start when there is no FC and a hot sunny day!