Ethyl alcohol is basically ethanol -- and I personally would be okay putting this on my dog's fur as it's not toxic in this manner, application, and amounts -- and bc it basically evaporates instantaneously, so it shouldn't / couldn't cause any appreciable problems or issues. It's sort of like using an alcohol wipe before getting a shot - it's a quick anitseptic but evaporates immediately.
I think you should be okay - but I totally understand your hesitation too. Here is a CDC link, but I'm not sure how helpful it will really be:
CDC - Immediately Dangerous to Life or Health Concentrations (IDLH): Ethyl alcohol - NIOSH Publications and Products