I don’t know what you are using your rainwater for out of that barrel. That would influence my decision some, but if you are leaving it open on top, lots of things are going on in there other than a squirrel. I get a lot of tadpoles in mine. I use dunks so at least I’m not breeding mosquitoes. I assume you are using it in your garden. Does it go on stuff you eat directly like lettuce or is maybe being used for something like corn? I’d probably drain it anyway because of the YUK! factor, but I’m not convinced that it would be necessary if it were going on something like my blueberries that are not in bloom or producing. If it were going on lettuce or something like that, yes I’d clean it well. But if it were open at the top I’m not sure I’d be using it on anything I was going to eat directly anyway.
What’s wrong with sterilizing it with bleach? Bleach is pretty effective if you leave it on there long enough to do its job. Just wiping it on and immediately rinsing it off is not totally effective but if you let it soak for a few minutes it does a good job of sterilizing things. It evaporated pretty fast. All you have to do is rinse it off and let it set a while. Even if you then immediately fill the barrel, it will be diluted to the point it won’t harm any of your plants.
Bleach is probably not organic though. I’m not sure. So you might try vinegar. That doesn’t do as good a job as bleach but if you put it on thick and let it soak, it will do a decent job cleaning it. I think vinegar is considered organic.