Presumably you've read Herodotos' descriptions of the Persian fleet and crews in Book VII?
"The number of the triremes was twelve hundred and seven, and they were furnished by the following: the Phoenicians with the Syrians of Palestine furnished three hundred; for their equipment, they had on their heads helmets very close to the Greek in style; they wore linen cuirasses, and carried shields without rims, and javelins…. "
Some Phoenician coins show dignitaries in Persian robes (see link) and right after the end of the Achaemenid period one interpretation of the Alexander Sarcophagus suggests that some of the figures in Median dress in the hunt scene are Abdalonymus of Sidon and some of his men. But if you look at for instance the figures on Phoenician scarabs (link) there is very little that looks Median or Persian.
"The Lycians furnished fifty ships; they wore cuirasses and greaves, and carried cornel-wood bows and unfeathered arrows and javelins; goat-skins hung from their shoulders, and they wore on their heads caps crowned with feathers; they also had daggers and sickles."
There is a lot of Lycian art from the period showing soldiers, though none of it bears out Herodotos' goatskin capes or feathered caps. Most of the soldiers dress like Greeks, but there are a few in Median costume, notably cavalrymen on the sarcophagus of Perices of Limyra or the Elmali/Karaburuan tomb – whether Iranians or local nobles in Iranian dress, who knows? But in the Lycian case Median dress does seem confined to the upper classes.
"The Carians furnished seventy ships; they had sickles and daggers, but the rest of their equipment was Greek."
Probably indistinguishable from their Greek neighbours, by and large. The figure labelled "Carian" among the throne-upholders on the Persian royal tombs at Persepolis has a Greek-style tunic and short cloak, and differs only in having puttee-like leggings below the knee.
"The Cypriots furnished a hundred and fifty ships; for their equipment, their princes wore turbans wrapped around their heads, and the people wore tunics, but in all else they were like the Greeks."
The Cypriots do not seem to have adopted Median costume very much at all: the Amathus sarcophagus (link) is probably typical.
