The paper: https://www.science.org/doi/10.1126/science.abm8868 The "soap and solvent" is sodium hydroxide (lye) and DMSO at 120 degC. Those are... fairly... well behaved chemicals, but lye is stout stuff and DMSO attacks nitrile gloves. You could imagine a remediation process that uses this process but the combo ain't exactly Dawn dish soap. I'd almost prefer pyroprocessing over it.
DMSO is used in pain relief in other countries (eg Mexico). It's also excellent for burns as it allows the body to repair a tiny amount of nerve damage or prevents it. Hard to say. This is demonstrable by burning yourself, I guess. My family and I have used it for burns for over 20 years. Granted, we don't get burned/encounter people who have been burned at home that often. I had a close friend with a rare disease (McCune Albright's Syndrome) who used it for pain relief, after I treated a burn she received.
It has been reported that it use has repaired massive nerve damage, which is probably coincidental. It is sold in healthfood stores in the US, but you want to dilute it 1/100 parts water. While it is primarily used as an industrial lubricant, on contact, it immediately travels through the skin to the nervous system. Most people get the strange reaction of the taste of oysters, when it's absorbed. There is a small percentage of people with various allergic reactions, like with many chemicals.
I would never mix it with soap, for any reason. It's like mixing shoe polish or granola with soap, you just end up with a mess of concerns.