I just read the account of the battle in De Bello Alexandrino, and there is no mention of how the Alexandrian troops were armed or armoured.
After reading this, I actually played a fictional version of the battle in the PC game Rome 2: Total War. In the game version, Ptolemy's troops are mostly native Egyptians, and mainly armed like Hellenistic pike phalanxes. Furthermore, the wikipedia article for the battle claims that the Alexandrians wielded pikes, but I saw no mention of this in the book and the wiki claims were unsourced.
Would Hellenistic troops still have fought in the old phalanx fashion, almost a century after Pydna? The author of De Bello Alexandrino mentions that most of the Rome's allies equipped and trained their soldiers in the Roman manner - would the Egyptians have done so as well, after so long under Roman influence?
This army, some 20,000 in numbers, consisted of men who had practical experience of fighting and a large proportion of whom had undergone Roman discipline, and were officered by Romans. Beside the troops of Gabinius (mainly, as we have seen, Gauls and Germans) it included a considerable number of refugees and escaped slaves from Italy and the West, and also a considerable number of bandits and pirates from Asia Minor and Syria — relics of the great pirate power broken by Pompey.
page 364 http://penelope.uchicago.edu/Thayer/E/Gazetteer/Places/Africa/Egypt/_Texts/BEVHOP/13*.html
Speaking as an ancient historian I'd say this scholar is probably near to the truth. By this period the Hellenistic monarchs were well aware that Phalangites (Macedonian style pike-men) were fairly obsolete against the Romans. Other Hellenistic monarchs of the period (Mithridates VI comes to mind (Plutarch, Parallel Lives 7.5)) hired Roman officers to drill their armies and outfitted them in this manner. The makeup of the of the local infantry would likely have consisted mostly of trained Egyptians either in the Macedonian or the Roman manner. That said the traditional pike-men were most likely still present (in what numbers and capacity are hard to say) and possibly held an elite role on the right flank of the army and by this period would have been mostly Egyptians. The Ptolemies also had a habit of hiring Galatian mercenaries from Anatolia.The cavalry would have been made up mostly of landowning aristocratic Graeco-Macedonians probably wielding lances as was the fashion in Hellenistic monarchies.
You raised the question whether Hellenistic troops would have still fought in the Phalangite manner almost a century after Pydna (148BC). Mithridates VI's troops (some of them at least) fought as pikemen during the mithridatic wars (89-63BC) not too long before the Alexandrian war (47BC). Given that Egypt was under such Roman influence however its likely they would have had more officers available to train their soldiers. Remember thought that 'Roman style' could mean trained as a legionary or it can also mean sword+thureos+thraco attic helmet etc (depending on the scholar you read..).
Sorry if this is a little slapdash, I could some sources for you to read if you're still interested. Hope this helps :D
Trying to find the source which E.R.Bevan is getting his information from ATM. How the slaves and pirates were equipped is up to guessing Though. The pirates that Pompeius 'conquered' were well equipped to say the least though.
TL;DR Essentially you're looking at Roman trained(sword and shield)+possibly some actual Romans, likely some Egyptian and Macedonian Pikemen (Macedonians would be rarer) and Greek/Macedonian style cavalry with Galatians (pretty badass heavy infantry) with some Pirates and Slaves.
Most soldiers would probably look like the Thorax Swordsmen ingame (or the Thureos Spears). Much of the Egyptian army was trained by Romans and it would have a distinct Roman "style". The Egyptians also hired many of the Celtic people living in Anatolia (The Galatia faction in the game). Cavalry would probably look like a mix between the Citizen Cavalry unit and the various Shock Cavalry units from the Macedon faction who were rich Hellenistic landowners.
The Macedonian phalanx was mostly died out after the Battle of Pydna, where the Romans demonstrated that they could defeat it.