Whose hands are these in Assassination Classroom chapter 179?
The poster and the scene afterward featuring Kayano strongly implies the female hand is hers.

It would sense that the person she was holding hands with someone that wasn't present at the old classroom building at the time, assuming that all the vignettes were happening more or less in real time.

The most likely conclusion would be that the male hand belongs to Nagisa.

After being questioned by Hara, Kayano didn't deny that they weren't together, and only mentions that he's focusing on his teaching career.

The anime skips this scene so there is no decisive conclusion, only speculation.