cnd, seems to me that these are unrelated tunes with related name, geographic i.d.

I know two variants of the Irish dance tune "Shoe the Donkey". It's a type of "mazurka". I am only familiar with Irish mazurkas and I don't know how they compare with the Polish mazurka. But Warszawianka is sung as a march and doesn't remind me of Shoe the Donkey. I can see and hear the close similarity between Varsouviana (Warsoviana) and Shoe the Donkey https://www.youtube.com/watch?v=o7Sx1_Q7iLw , https://www.youtube.com/watch?v=yrPvLBjfQ_Q but not with the Warsawianka song.

note the difference between the song (French version, La Varsovienne)
https://www.youtube.com/watch?v=T5BllldNrf4 and dances (I found a few variations of the Varsovienne dance on youtube; this Scandinavian version has some similarity to Shoe the Donkey) https://www.youtube.com/watch?v=xRKP493ipN8