I believe the arrows are accessible as anonymous child frames of the minimap (i.e., with no global names).
I haven't messed around with them for a long time, but they used to be model frames. It might be possible to hide them by iterating through the minimap's child frames, checking to see if it's a model frame, checking to see whether its model is the directional arrow model, and then hiding it.
Those frames are probably created and recycled dynamically, so the hiding would probably have to be done constantly using a timer. This might get rather CPU intensive, for example in a raid where you have 10 or 25 or 40 of those directional arrows indicating raid member positions.
In the end, I think learning to like them will prove to be a better experience. :)