That would be no.
That includes Crazy Glue™, Loctite™, airplane model glue, and Elmer's™ glue as well as any other glue that is not specifically labeled surgical glue.
It is a myth that this type of non-surgical glue was discovered accidentally during WWII on a battlefield to address wounds. In 1942, it was an attempt to find a way to glue the plastic gun sights on rifles.
Non-surgical glues contain methanol. It is toxic to tissues. You are potentially adding a toxic substance directly into the blood stream. Surgical glues use medically safe bacteriostatic esters.
The other problem with any type of glue (surgical or non-surgical) is sealing in bacteria, which may result in abscesses, staph, or sepsis. There may also be damage to the cellular walls slowing healing.
Waivers and verbal OK's from clients may not stand up in court. A good lawyer will argue that the client was not duly informed of the dangers to their pet.
But don't take my word for it.
"Using surgical glue to close a wound is considered a medical procedure. Unless you are under the direct supervision of a veterinarian you are opening yourself up to legal action. - Dale Krier DVM Creature Comforts, Sherman, CT
"Superglue is not medically safe and you can introduce toxins into the body. Surgical glue used improperly may introduce bacteria and cause abscesses. Either way, you may cause serious life threatening injuries." -Kaely Blum VCA Northside Animal Hospital, Danbury, CT
Gluing injuries potentially can open up a huge cans of worms for your business. And you may want to check with your insurance company to see if you are covered for injuries resulting from what is considered "practicing veterinary medicine."
A better plan is to have a good relationship with an area veterinarian who could walk you through this medical procedure (direct supervision) in the event of a life threatening injury that you are too far from the nearest veterinary facility to make it in time with just wrapping the injury.
Mary Oquendo helps pet professionals achieve their goal through easily accessible online education, as well as one on one business coaching.