Forgeworld's rules tend not to be as robust as Games Workshop's (which is saying something, given the common lack of robustness of Games Workshop's rules) but I think it's fairly clear you use the Eldar Wasp Assault Walker entry.
Corsair units do not have the Eldar Faction, and the Wasp Phalanx is one of the Formations for use in the Eldar Craftworld Warhost Detachment, suggesting it should be of the Eldar Faction. Also the Formation calls for 3-6 Wasp Assault Walker and the Eldar army list entry is 'Eldar Wasp Assault Walker' while the Corsair army list entry is 'Corsair Wasp Squadron'.
The Formation says nothing about them becoming one vehicle squadron, so they are independent.
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