I think Orajel USED to contain Benzocaine chloride, which is soluble in water. I think it was changed a while back to Benzocaine, which is not very soluble in water.
As a result, the new product would be poorly, very slowly, absorbed through the skin. It is soluble in ethanol, and in acidic solutions. Maybe the polyethylene glycol in the ingredients is to make it water soluble, in which case it would still be effective.
Mixing a bit of ethanol into the orajel would increase absorbtion, but I don't know if ethanol would sting on frog skin.
Euthanasia is awful stuff to think about. I know it is for the best sometimes. But it is very hard to think about it.
H