In many Botei Medrashim/Yeshivos, some of the Nigunim during Hakafos are Yiddish Nigunim (Gits Arein, Olam Habo etc.)
Reb Iser Zalman Meltzer Zt"l used to sing during the Hakafos the song “Kometz Alef Oh Kometz Bais Boh- and the song
“Omar Abaya”. R.Isser Zalmen said these were the Nigunim
they sang in Volozhin Yeshiva during the Hakafos.
In some Ashkenaz Shuls, they are Makpid not to sing any
songs with Pesukim . They sing only the Piyutim printed
in the Machzor and Nigunim without words.
It is very likely , that in the olden days they would not sing Pesukim and therefore sang only Yiddish Nigunim etc.
Many are not aware there is an Issur to sing Pesukim.
They are also not aware that the Poskim tried desperately
to justify why almost everybody sings Pesukim and are not
concerned with the Gemoro – התורה חוגרת שק- עשאוני
בניך כמין זמר .
Reb Moishe Feinstein writes (Igros Moshe Y.D.2: 142) He doesn’t know of a good reason to justify it.
R. Chaim Kanyevsky Shlita holds one may only sing Pesukim
If the intention is to praise Hashem. Singing Pesukim for Simcha is forbidden even for Choson/Kallah.
Reb Elyashuv zt”l is Matir if one's intention is to pronounce with the Nigun the meaning of the words ,for instance, מה אהבתי תורתך then one is allowed to sing.(The music should match the words and help in the Kavana).
There is also a problem singing the Piyut of האדרת והאמונה on
The Mogen Avraham writes (O.Ch. 565) one may not say this
Piyut ברבים except for once a year on Yom Kippur.
Could be that by adding the Yiddish words צוא וועמען צוא וועמען
might solve the problem.אמבצי