The Rebbe explains that saying Chazak Chazak VeNitchazek upon completing a Torah reading is not considered an interruption, as it pertains to the conclusion of the reading (Shulchan Aruch Admur HaZaken 667:9). He also notes that our version of the phrase is VeNitchazek.
https://www.torahrecordings.com/rebbe/004_igros_kodesh/tishrei/779