According to Plumb's veterinary handbook, Dimethyl sulfoxide is a safe drug to use, when used as directed. The concerns of toxicity are mainly focused on the intramuscular, and intravenous injection of dimethyl sulfoxide. DMSO is not something I use often, but if I do have a bird with a severe limp, I may apply the DMSO to the leg to help reduce swelling. It can also be used in cases of prolaspe. It is best only used a few times, as repeated use can affect the underlying cell tissue, and recent literature I've read suggests diluting the gel/liquid down with water halfway.
Many people use DMSO for their aches and pains. The cautions that are stated for it not to come in contact with your hands is merely a safety issue to prevent lawsuits if a reaction were to occur. I do wear gloves as a precaution.
https://www.beautyofbirds.com/medicationsexotics.html