In brief... The Military nurse like most orderlies and attendants were folks detailed or assigned from the ranks. So most wouldnt have any special uniform or insignia for the most part. (less you were detailed to the Ambulance Corp etc) Many of these "nurses" didnt have any real acedemic medical training so for the most part were extra hands around to assist the medical staff. Unlike the modern image of a nurse as mostly being female and the Florence Nightingale aura, Majority of Military nurses were male, especially in the early parts of the war. The female nurses were reluctantly accepted into the established status-quo of the medical field out of necessity more than intended desire. As the social mindset of the era as it was thought to be somewhat reserved to allow proper ladies to be in such a location whereas men in various stages of undress, pain and torment would be improper thing to do and allow. Of course that changed over time. But in the field most orderlies and "nurse" roles predominately remained a male role task.
All you would really need for it is your normal uniform attire, then up to you if you wish to make use of an apron or other misc related items. It would be a good role to learn from since you can sit back and listen and learn from others if you have a knowledgeable medical staff to work along with. Good luck...
Lieut Frederick Sineath
14th Virginia Infantry Regt Co.I
- 106th Penna Vol Co.F