shaking hands

I previously worked at a surgical center as an RN surgical assistant, where one of our tasks was giving SQ lidocaine on faces, and everywhere else on the body for surgery. Sometimes, my hands would shake when giving the injections. I worked there for 6 months, and I guess my insecurities, nervousness about the job would show in that way. I was asked to resign because of other minor things.  One of my nightmares after that was thinking I could have poked someones eye out.

After that, I did a year in LTC, and some time in private duty nursing. 

8 years later, I have never had shaky hands after that job.

I would like to apply a nurse residency for the OR in the hospital and was wondering if that's something that would affect that job. I don't think I would have shaky hands since I'm not giving SQ injections on a patients face. 

I'm also worried about the application part for checking the box if eligible for rehire. Would checking no be the kiss of death?

TIA