The sources actually aren't totally silent on this issue, and for general coverage of it you can see David Whitehead, "Who Equipped Mercenary Troops in Classical Greece?" pp. 105-13 in Historia 40, 1991 and Paul McKechnie, "Greek Mercenary Troops and their Equipment" pp. 297-305 in Historia 43, 1994. These deal overwhelmingly with the case in the 4th c. BC, but there are also a few excurses on the 3rd c. BC. Unfortunately, all the literary evidence is far too vague and scattered to be able to form any consistent image of the arming of mercenaries.

For less explicit evidence, yes we have sources of information like the Alexandrian and Sidon stelae, but those two are unfortunately contradictory. The Sidon mercenaries seem to have been fairly uniformly equipped (at least when it came to thureoi and helmets), but the Alexandrian mercenaries certainly weren't and seem to have been armed in their native panoply (Galatians being the most prominent group, obviously).

That reminds me, would you happen to have information on that papyrus that Thompson mentions in Memphis under the Ptolemies which refers to a 10-drachma annual clothing stipend for Ptolemaic troops? I think it was 3rd c. BC in date, and she mentioned that it was unpublished, but that was obviously in 1988 when the book was published. I'd just like to know a little more about it and if we can tell if it refers to mercenaries or standing troops. Any idea?