Maybe the term "heavy" on battle axes is being mis-applied. I mean heavy compared to a hatchet, not heavy compared to an automatic transmission. Don't get into the fantasy thinking of an axe as big as a stop sign - a heavy hand axe is three pounds tops.
The Arabic peoples used plenty of various axes and maces around the time of the Crusades. Even if their traditional form of combat was lightly armored cav and sabers, they had to adapt to the heavier armor of the European troops. (More specifically, the more frequently armored European troops - their individual armor was no heavier, just that a larger percentage of their army was wearing it.) The various Arabic clubs and maces were quite common, as you will find them in the mod... and are some of the Middle Eastern and central Asian axes, such as the Ghulam Axe in the screenshot.
Due to some minor internet interference, I can't find a picture of one ... "page cannot be displayed" ... but some of these axes have survived and can be seen in museums here and there. The model seen in the screenshot was in use from the late Roman period to after the Crusades, more or less unmodified. Seen more often near India on the other side of the old Persian empire (Sassanid Dynasty - source of the term Ghulam - "servant boy"), but still used extensively in the Crusades by troops of the Abbasid Caliphate.
Egypt has a very long tradition of arming shock infantry with hand axes, dating back to the Old Kingdom. The long, narrow curved sabers (like the "Mamluk sword") are a relatively recent addition - being phased in 10th to 12th century. Long curved sabers were really not that common in the time of the Crusades. The straight-blade seif was about the closest thing to a saber in common use.
In general, spears (or related polearms) and bows (or crossbows, and later firearms) were always the first line of defense. Swords, hand axes, maces, daggers and knives were almost always backup. Some forces were trained to go to the backup quickly (i.e. the Romans who threw the pilum and then drew swords), while others tried to stay with the primary as long as possible. The idea is usually not to get that close, if you can avoid it.
Still, the Mamluk and Ghulam, among others, carried hand axes or maces as backup weapons. This was also the high point of the mace in Europe, much the same way.
Check out the mod. It will be ready soon. I think you'll find the number and type of weapons to be pretty accurate.