Is it possible to use the Unity Panel (with or without launcher) with i3-wm instead of compiz?
And if that's not possible, could I somehow use the HUD inside the i3 session?
This is not possible with the true Unity 3d environment. Unity is actually a compiz plugin running an Openbox toolkit called Nux, so to attempt to run Unity without compiz is an exercise in futility. You could check into Unity 2d, however, which has a similar appearance, but is a separate set of packages not dependent on Compiz.