Hmm, yes let’s be pedantic 
PoE is 57V max. Dry skin is around 100kΩ, while wet skin is around 1000Ω. So depending on how wet hands, your skin will conduct between 0.57mA and 57mA at the most (current, not power: it’s current that kills you).
If you’re unfortunate enough to touch the source with both hands wet and that current reaches your heart, you might die. If you grab a stripped ethernet cable with wet hands, you might not be able to release it. Otherwise, most likely you’ll get a good jolt, is all. That’s if the source even reaches 57V in the first place of course.
And of course, none of that current will ever flow through the chip.