I unfortunately did not find the etymology of Ukranian word зозуля zozúlja cuckoo. May it be a satemization ?
As Jk wrote in his answer, the regular sound changes stop working regularly when it comes to onomatopoetic words. However, it does not mean that the sound changes do not occur and cannot be researched.
To give you some data points, here is the article from Vasmer's etymological dictionary which lists some possible cognates from Slavic, Baltic and Germanic languages. (I have translated the language names and key words from Russian to English, but not the references)
GENERAL: "cuckoo", dialectal жегозу́ля, заго́за (Novgorod), заго́ска, зазу́ля, зозу́ля, Ukrainian зегзи́ця, зезу́ля, Belr. зозу́ля, зязю́ля, Old East Slavic зегзица (СПИ), зогзица (Срезн. I, 994), also жегъзуля (Толк. Палея; см. Соболевский, Лекции 143), Chech žežhule, Slovakian žežhulica, Polish gżegżóɫka.
ORIGIN: Pra-slavic *žеgъzа with various distant assimilations; cognate with Lithuanian gegužė̃, hence gegà, gẽgė, Latvian dzęguze, Old Prussian geguse, further: Old Icelandic gaukr, Old High German gouh; see Меіllet МSL 12, 213 и сл.; Trautmann ВSW 81; Аltpreuss.Sprd. 336; М.--Э. 1, 539 and futher. There is no reason to assume borrowing from West Slavic into Russian, contrary to Bulakhovsky (ОЛЯ, 7, 108). Doubts regarding the affiliation of the Old Icelandic gaukr see Holthäusen, ZfslPh 24, 451.
As one can see, palatalisation might play a role transforming former g into z or ž, but in that case it happened in the Balto-Slavic period, long after satemization.
Words like cuckoo or зозуля zozúlja are onomatopoetic and thus impossible to tract by historical linguistic methods. Because they are linked to natural sounds (in this case the call of the bird) they do not follow the regular sound laws. They also tend to be re-created anew ex nihilo (i.e., just from the natural sounds they are imitating).
TL;DR Nothing conclusive can be said about this one.