Hi Dan,
Something that I have done in the past that might work in your setting to help students overcome their fears in certain settings is to pair them up and have them work together on a procedure. This pairing helps the in that they are not in it alone, that other students have the fears as do they and that can use each other knowledge and experience to get through the activity. I have also had the demonstrate the procedure after they have practiced it a few times. This really helps to build their confidence as they start to see that they know more than they think they do. One success then leads to more successful and more self confidence and self esteem.
Gary