Stair renovation - filling gaps

[Eligus]

Hi! We're working on our staircase, an endless job of sanding after removing the old plastic mat.
We have these gaps on almost every step and since we're not going to put down a new mat to cover them, we're wondering how best to fill them in?
Someone at the paint store mentioned latex caulk, could that be an option?
The steps will be stained dark while the risers and sides will be painted light...

 

[Eligus]

 

[MrDizzy]

Personally, I would probably choose wood filler / Chemist wood instead of latex.