This may not seem like a very important question to you. And you’d be right.
This question came up, and I assumed yes. Cells do, generally. Cells absorb O2 and produce C02 … even plant cells do this … through passive systems. But I wondered if the fact that the epidermis is adapted to be a barrier might mean that it would not. But then I realized that the epidermis absorbs water. O2 and H2O both diffuse freely across cell membranes. So of course some of the cellular respiration in mammals is surface diffusion. It must be. (Warning: I don’t know this to be a fact. If you do, state so in the comments and provide a reference that you’ve actually read recently and can verify, please!)
The problem is that when you “google it” … ask the Internet if humans or mammals absorb any oxygen through their skin, you get an interesting result, an oft repeated phrase: “No. Human beings cannot usefully absorb oxygen through their skin.” Which is not really an answer to that question, is it? I wasn’t asking about “usefully.” Jeesh.
I’m pretty sure that the answer to the question “do humans absorb Oxygen through their skin” — which is clearly a yes or no question — is “yes.” But perhaps this leads to concerns that some of the dumb-ass humans will misuse this information thinking that we actually breathe through our skin in any meaningful way. Imagine the stupid Darwin-Award wining tricks people might think up to do with this factoid. Nonetheless, while “the widely held mis-belief” that humans “breathe through their skin” is a potentially dangerous concept, it is also simply true that all typical normal living eukaryotic cells respirate. Even plant cells “breathe” in O2 and “breathe” out CO2. So the answer “no” isn’t really acceptable.
In truth, the best answer to the question “do humans breathe through their skin?” is probably something like “Please re-phrase that question so I know what strange and inappropriate things will happen in your brain depending on the answer”