There is no way I would do this without proper ventilation and at least an N95 mask. I do paper towel paper mache with gravity. Spar urethane with a mask on as well would make it plastic-like. I like what he's doing, but mask up if you like your brain and lungs. Wear that mask for the stain as well. Eye protection might be a good idea too. Damn, those fumes must be killer!
What kind of flesh? what kind of props? does the "Flesh" need to flex for a moveable prop or is static OK? What works great in one scenario may not be the best on another. Plastic (as in the video) works in some cases, other times Elmers glue and bedsheets, latex, rubber cement and panty hose, A/B foam, Silicone, all of these can be made to look like flesh, it really depends on the application and budget. The easy answer which looks great is silicone, it moves well and has the translucency of real skin. You can add flocking to it to simulate cappilaries and airbrushed veins seem to sink below the surface if applied correctly. Platinum silicone is also around $240 a gallon- so it is not the cheapest option.
the only fumes from this are from the wood stain, and they really arent that bad. You arent burning the plastic, just shrinking it. If you try really hard you can coax a few fumes, but its pretty difficult.