You mean aside from previous injunctions when deriving "pteridae" from "pteryx" or "pterus" as wehn *Caudipteridae* is used? Forgive me, but my understanding is that regardless of -pterus or -pteryx, -pterigidae is the "correct" modification (as far as convention stands).
How did you get that idea? _Pteryx_ is _pteryg-_ with the nominative singular ending _-s_. (To add another example of how this works: AFAIK, the genitive singular ending would be _-os_, so the genitive singular would be _pterygos_, and so on, but I don't know Greek.) The ending _-idae_ is added to the stem _pteryg-_, giving _pterygidae_.
(BTW, i and y [iota and y psilon] weren't pronounced the same way in Classical Greek. That's why the letter Y was introduced into the Latin alphabet at all.)
_Pterus_ is _ptero-_ with the nominative singular ending _-s_ and the fact that unstressed short _o_ turns into _u_ in Latin. The ending _-idae_ is added to the stem _ptero-_, but the Romans didn't like vowel clusters, so we don't get _pteroidae_, we get _pteridae_.
-Pteridae is a matter of some sloppiness that crops up in other Chinese taxon names, even when using -pteryx as the source which is then modified.
_Those_ cases, like Caudipteridae, _are_ wrong.While I am at it: _ornis_ is _ornith-_ with the nominative singular ending _-s_ plus the fact that _ts_ turned into _s_ in the 8th or 7th century BCE in Greek. The genitive singular ending _-os_ is added to _ornith-_ to give the genitive singular _ornithos_.