I'd focus on controling that anxiety and self-consciouness in addition to fluency techniques. The anxiety will make your stutter way worse and may make harder for you to remember the information relevant for the case or to construct your phrases in a coherent way. Your goal should be giving a good answer to the question the professor asked you, stuttering a bit or not. Also linking your anxiety to your fluency level will only make your worst day a total nightmare and it gives your stutter a enormous snowball potential (I've been there and it sucks). My advice would be become confident talking in front of a large group of people. So pick your poison: Go to open mic nights, join a casual troupe, read at your church/whatever...