would like to use tablet mode
I think you may be confusing two meanings of "tablet mode". In Windows 10 you cannot have multiple displays and use its tablet mode. However (as I understand it) your Surface Book can be used without its keyboard, so if that is what you mean by "tablet mode", I think you could use it with a second screen but not with Windows 10's tablet mode.
BTW notice that W10 now has a thing called Touch Pad button in the Taskbar. So, I imagine that you could use that on your tablet screen to move a pointer on the second screen, without having a keyboard attached. Otherwise, there is a way to use your tablet screen's touch screen as a means of controlling stuff on the other screen but it is pretty ugly and you have to be both skilled and lucky to be able to do anything useful that way.
Edit: I just realized that there is also Project Duplicate which would allow you to use your tablet's touch screen and see what you were doing but depending on the resolution of the projector and the orientation of the tablet that might not look very good. In any case, I think there are definitely ways that you could show stuff on a projector and control it with only your tablet's touch screen but I would recommend a trial before the show. ; )
HTH
Robert Aldwinckle