An interesting scenario. A couple of questions occur to me. What is the water source which the Mycenaeans are intending to occupy and exploit? A desert well? A desert village with a well? A wadi with ground water near the surface? An oasis? It occurs to me to ask you why the NKE forces are trying to block access to the water source rather than simply occupying the water source themselves and forcing the Mycenaeans to fight on the Egyptians’ terms. Is there some other consideration which keeps the Egyptians from occupying the water source? The Shasu might then be used as scouts mounted on mules/onagers/camels and as a foot-screening force to warn the NKE of the Mycenaeans’ approach or to harass and exhaust the Mycenaeans before the battle. The flank arrival being them catching up to the Mycenaeans as these foreigners meet battle with the main force.
You say the Mycenaeans will be fielding cavalry? Aside from mounted scouts would it not make more sense for them to field chariot units rather than proto-cavalry at this early time? Why go with cavalry? If the terrain is rough going would any cavalry or chariots be appropriate?
What kind of terrain will the battlefield be dominated by? The terrain could make the difference in the game. If it’s flat and open then the NKE forces will be at a big advantage. If the terrain is more broken and rough then the NKE chariots, archers and close order infantry will be far less useful, the Shasu more valuable and the Mycenaeans might enjoy a real tactical advantage.
I’m looking forward to learning more about this proposed battle as you flesh out the conflict more fully.
Cheers and good gaming.