Maybe something with lactic acid like buttermilk, yogurt or cream? Even if you can't eat it its supposed to be good at softening the skin and exfoliating the top layers. I get spots if I eat it but topically its good on my skin...weird. I've used Peter Thomas Roth's AHA without much irritation too but I don't have really sensitive skin.

I find that a salicylic/glycolic peel once a week or twice a month works much better than a chemical exfoliate used more frequently.Chemical exfoliates tend to really make my skin angry, but if I space out 10%-25% peels, Not sure if they are animal free, but you can buy both kinds of peels online and dilute with water.

Viviant Skincare Exol-A. I just made a post about it. Out of the million products I have tried, it's by far the best. It's pricy but it really worked for me.