Fantastic. I don't see it being a problem. I do my best to keep gloves on me anyhow, just in case, and I'm very attentive about wearing them for safety - both mine and yours.
The reaction is not an uncommon one at all. I tend to use a light sedative and prefer to work with a local anesthetic if needed. But I've been told my bedside manner can be quite soothing. I will do my utmost to make sure that if medical attention is ever needed, you're as safe and comfortable as possible.