n3K3/8/B7/7p/8/8/8/k2N4 w - - 0 1
Yeah, exactly right!! 1. Kd7!! - White kills two birds with one stone by limiting Black King’s mobility and trapping Black Knight. Kudos to Alena!!
Yes, 4.Nc3 in the line Alena gave is a truly beautiful move in this puzzle.
The "most resistant line" you give, Alena, is quite beautiful as well as being somewhat humorous, with the White knight cutting off 2 squares for the Black king and 2 squares for the Black knight, as well as the Black knight cutting off the remaining square for its own king.
Bc4! If knight ...b6, Bb3 and the plan to me looks good.
I think It looks like the most resistant line.