The only specific source I know is a small booklet by Anton Wlodzimirski "History of cold steel in the Ukraine", Donetsk 1996.
According to him, there was never a specific Ukrainian style: cossacks used " ... Polish, Hungarian, Turkish and Caucasian sabers. Later, Russian sabers of 18-19th centuries became widespread , such as the light cavalry pattern 1809"
Wojciech Zablocki, in his book " Ciecia prawdziwa szabla" , Warszawa 1989, discusses Polish sabers Type III and labels one of them (shown below, the Right-most one) as " Kozacka". This is also unlikely to be specific, however, in view of the irregular nature of the Cossack troops.
In the famous picture by Repin " Zaporozhians write a letter to Turkish Sultan" one can see a variety of sabers, especially Kilij and shamshir-type.
http://www.allartclassic.com/subj_pi...EI001&forder=1
Even taking into account the late 19th century date of the picture and the usual "artistic license" with the props, this likely reflects the reality.