Can one say tachumun during haazaras ha shas if it will finish after Shkia and his custom is not to say tachumun after Shkia?
You are allowed to say tachanun even after shiya, until tzeis hakochavim. The minhag Yeruushalayim however is not to say tachanun after skiya. In that case, or oyu minhag otherwise is not to say tachanun after shkiya, if the chazan will not finish in time, it is better not to say tachanun than to say it in middle of chazoras hashatz. The reason being the tachanun is considered a reshus, therefore it shouldn’t be said in middle of chazoras hashatz.
M:B 31-17, Tefilh Khilchoso 18-ftnt 64 in the name of R’ Eliyashiv and R’ S. Z. Auerbch zt”l. R’ Nutrani Gaon brought in the Tur O:CH 131, Taz ibid 11,