What exactly do you mean by 'Egyptian Askari?'
If you mean Egyptians from the Mahist wars of the 1880n I would say not. Cut of the uniforms is all wrong. Force Publique either wore trousers that stopped at the calves and went bare-legged below that (pre-war uniform), or wore puttees that entirely covered their calves (later war uniform). Neither of which looks like an 1880s Egyptian. The jackets and equipment are pretty different, too.
Though maybe you have some other Egyptian figures in mind? Not entirely sure what else is out there in the world of 15mm.
Egyptians of the 1890s would be a slightly better fit, having at least got puttees. For the Zoauve look of the early war Force Publique I think your best bet would indeed be actual Zoauves, either ACW or French ones. In 15mm nobody is really going to notice the fact that they don't have African facial features.
As to Diablo Jon's suggestion, I don't think the Force Publique wore shorts during the Great War, though I know they did in WW2. But the overall look is pretty good. Perhaps the best idea yet. They don't look very Zoave-y though, so I'd paint them up us as wearing the khaki uniform, or the intermediate one of a khaki vest and blue pants.