I used to work in the R&D division of a large US company that makes lots of formulations to test that may become shampoos, lotions, conditioners, etc... The goal of my boss's research was to try to come up with a lab test that would predict with some accuracy how irritating a formulation would be to someone. They traditionally do lengthy and expensive clinical tests on people who rate the formulation's pain and irritation on a scale. A lab test could predict that would be far cheaper to the company.

Ok, that was a long intro. Point being, I was one of the people who received surgical skin explants (they are called explants), ours was usually from tummy tuck surgeries. I would get a big hunk of it, and have to cut all the fat underneath off. I splayed it out as flat as I could, and using a very sharp scalpel, I cut it into 1cm x 1cm pieces. All of this was done on ice, to keep it cold and alive.

I would then apply treatments to the outer dermal layer (the top), the treatments were lots of positive controls (capsaicin, hydrogen peroxide, formulations known to be irritating to people, etc...) and negative controls (water, water with DMSO, formulations that were known to not be irritating). And we'd let the skin sit with the stuff on top overnight. Next day, I'd flash freeze it in liquid nitrogen, then cut it up in ~20micron slices on a cryotome. Put a bunch of the pieces on slides, and then stain the slides with various things. Most often using a technique called immunofluorescence, where you add a mouse antibody to the slide to bind to a selected protein, and then add a fluorescent tag to the antibody. We'd choose proteins that we thought were upregulated during inflammation and irritation. Then I'd quantify the amount of fluorescence spending days in a dark microscope room staring at dimly lit slides.

But to the point of there being a market for human skin, there is not. Human skin is an organ, and as such it cannot be sold legally on a market, it must be donated. However I would believe that companies like the one I used to work for might have subdivisions that would perform surgeries for free and encourage the patients to donate it for research.