For the most part I've ignored the specifics of individual units, since I've been focused on entire classes of them (javelineers, secondary spear users, cavalry, etc), but this is one that's jumped out at me. I have a sneaking suspicion that as an expediency the Akontistai model has been re-used to do the Hippakontistai. A knife as a backup weapon is fine for psiloi, especially since they represent the poorer members of a poleis, thus that's all they'd likely have.
However, it doesn't fit for Hippakontistai for two reasons. The main one is that any man who owns a horse (and by implication remounts, since a man isn't a cavalryman unless he has at least two, or better yet four horses) is not poor. Hippakontistai are a call-back to the older form of Greek cavalry before Philip of Macedon, where the aim was to be mobile, harry routers and be able to flee if things went badly for the poor buggers in the phalanx. A man who can afford a horse can afford a sword or spear as backup. Secondly, a knife is useless on horseback, it's too short to reach anything. Holding back a heavier javelin for melee would make more sense than something not much longer than your hand. The kopis was a popular weapon for this sort of cavalry (mentioned in Xenophon and indeed was the model in EB1), and would have been well within the budget of a man who can afford horses.
Here's the relevant bit off the EB1 website:
What happened?Hippos Akontistes (literally "javelin horsemen") are the standard among Hellene light cavalry. They are lightly armored, often wearing nothing but padded cloth for protection. The key to their method of warfare is speed, and they are armed accordingly. They ride small, but swift horses and harass enemy infantry and heavy cavalry with javelins. This is their primary use, because their light armor is really a detriment when they are engaged in any kind of melee combat. Their swords and shields are simply no counter to lances or heavier cavalry swords.
Historically, Hellas did not have a great tradition of light cavalry warfare, or indeed of any cavalry warfare. Hippakontistai were much like the Equites of Rome, the spoiled children of the richest families that could afford horses. They were usually not used in any front line capacity other than skirmishing and pursuit, and their equipment reflects this. Makedonian cavalry of the same type operates in a similar fashion, but generally comes from the poorest noble families, those who can afford horses but not the heavy armor required for the heavy cavalry