Physical Danger
You aren't dodging bullets, fighting angry bulls, or operating heavy machinery. You are, however, around a lot of chemicals. Sure, you may preach the virtues of a natural, organic skin regimen, but some of your clients won't want that. Some of your clients will want you to burn their skin to a raw, red crisp using strong chemicals.
There's a reason estheticians limit chemical peels to a maximum of thirty percent alpha hydroxyl acid (source). Considering that alpha hydroxyl acids are "safe" at concentrations of under ten percent, and considering the fact that the whole point of chemical peels is to irritate your skin, you can also expect some irritation, redness, even sensations of burning. Even if it's not your chemical peel.
Generally speaking, though, it's your patients who need to be careful—not you. (Well, you should still be a little careful. Burning your customer will burn bridges with your clientele, which will burn a whole in your pocket.)