I did attend my class 2 days ago, and even did uke for my teacher, only attacking with the right hand. As far as the right hand, everything is OK. I keep my left a bit folded but otherwise the lesson went OK. My classmates accepted me attacking with the right hand only and being attacked likewise.
I will also attend tonight's lesson and see how it goes...
I understand that you cannot use your left arm, you have 'only' managed to adapt a little. Like Mario says, and myself, have your exam put off until your arm has healed.
I can imagine this exam is pretty exciting/important. Black belt is always some kind of milestone, no matter what style you are in. But I do not think it is more important than your well-being. Budo, the mother of martial arts, says self-preservation is most important.
Making the right decision is hard, but is ultimately that what builds (your) character