About 40 years ago I boarded my horse with an old cowboy who used DMSO as a horse liniment. He had been using it for years any time one of his mounts was worked pretty hard or when someone brought a lame horse to him. He would rub the joints, calves, and thighs of the horse down good with DMSO for a few days and then they were good to go again.
He also used it on his wife. He told me that she had type I diabetes and neuropathy as a result. Her feet were always cold from poor circulation. That was true until he happened to rub her feet one day after treating a horse. Her feet warmed up in minutes and became normal pink again. After that, he used it on her feet and legs since it improved circulation.
You can say what you will about it being reactive and possibly not good for you but she was able to dance again and get back on her horse so it definitely does have some benefit. They did this for at least 30 years and both of them were past 75 years old when they passed away.
Like another poster said, it is used as a carrier for some medications since it pulls them straight into the bloodstream. I don't think it's magic but I also don't think you'll suffer much using it even with bare hands.
As far as lye is concerned, the sodium hydroxide in this paper, you can easily make that yourself with wood ash and water. It is pretty handy if you are tanning hides since the treatment of a raw hide with lye causes the hair to slip right off leaving a smooth skin ready for the next step.