I take it that the term machimoi didn't imply any kind of special equipment. So most New Kingdom era ranges might be useful, right?
First off there's the well-known
stuff by the Perry brothers at Wargames Foundry.
Black Tree Design have quite an extensive and nice looking
range of New Kingdom Egyptians. (And yes, I explicitly recommend BTD for their excellent service.)
1st Corps had previewed a few Ptolemaic phalangites
here, which are part of their
Successor range. Perhaps worth a look for conversions.
A few tasters that sprang to mind. Nothing that comes with Assyrian shields per se, however.