к/ч consonant alteration is the result of Slavic first palatalization. It happened because inherited velars *k and *g had no soft counterparts in Proto-Slavic, so they changed before front vowels *e/ē, *i/ī, and also before the palatal semivowel *j.
Researchers argue about dating of this process. Some believe it happened during VI-V centuries BC, and some postpone it to V—VI CE. I found no direct evidence, and I'm not a specialist in language or Slavic history, but it seems highly unlikely to me that this process had Uralic influence.
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