Catapults might have existed - I dunno. But, that brings up another question - was the area yet forrested?
SC, Blam?
The Delta was and is forested, just not oaks, maples, and the like :’). The Egyptians built very large structures of mud brick (as someone pointed out) but for defense relied on fending off attacks with sheer numbers. The other big defensive array was the Sinai. Crossing that was done all the time, by merchants, shepherds, the Children of Israel, and whatnot, but it was non-trivial to march an army across it. Nevertheless, Egypt has spent quite a bit of its history (despite what Hawass et al claim) occupied by foreign powers (possibly the Akkadians, the Hyksos, the Assyrians, the Persians, the Macedonians and Greeks, the Romans, various foreign Moslem caliphs and sultans and whatnot, a couple of different European powers).
Like a lot of insular powers throughout history, Egypt’s worst enemy may have been the internal power struggle.
Egyptian soldiers used shields occasionally, but mostly relied on bow and arrow, spears, and small specialty units used slingstones. Use of artillery (that is, catapaults and related doodads) may not have entered Egypt until Alexander the Great, or perhaps the Persians before him. Phillip (A’s dad) used “belly shooters” which were powerful crossbows which IMHO fall into that category. The Romans used artillery for siegecraft in a lot of campaigns of conquest (Vespasian was particularly skilled in its use, and reduced dozens of hilltop forts in Britain), but the Roman conquest of Egypt was a pretty quiet affair.
By the peak of the New Kingdom Egyptian higher-ups relied on chariots, and as in most ancient users of war chariots, these were mobile artillery platforms, allowing the attackers to zoom up, shoot off a (largely randomly targeted) volley until the “ammo” was used up, then turn back toward Egyptian lines.
Anyway, the use of wood in Egypt was in construction (various ways), furniture, boats, and the arrows, bows, and spears mentioned. I don’t think they relied as much on dung for fuel as the Mesopotamians did.