Usually after Hallel the Chazan says Kadish Shaleim, however on Chanuka (not the Rosh Chodesh days, or Shabbos day) we say only Chatzi Kaddish, since there is no Musaf later. If a Chazzon said in error Kadish Shaleim should the Chazzon say Kaddish Shaleim again after Ashrei/Uva L'Tzion as usual or should there be some change in that Kaddish? (sources)
Based on Rav Eliezer Melamed (Peninei Halacha Tefillah 23:2 fn3) where one said Kaddish Shalem after Tachanun, he quotes Ishei Yisrael 26:5 who says to skip the "Tiskabel line" when Kaddish Shalem would have been said. This should equally apply to our case as well.