As the Turks you can send Hassan ibn Sabbā and his becamel'd legions of death against Egypt. Don't worry about the Nubian Spearmen. Just charge them from the flank and the whole lot will be routing. It's a good idea to target and rout his peasants first in any given battle, this will demoralise the other nearby non elite units. In the past I've beaten Egypt using the Sultan's ransom method using only Vanilla HA's and camels. I've also beaten the Byzantine using much the same with an additional few AHC and vanilla spearmen, so it can be done.