Is it okay to cut the foam cleanser with scissors before using it?

Usually, leftover facial cleanser or toothpaste is

Cut it cleanly with scissors and use it neatly.

They say there is a risk of contamination because the cut part is exposed to the air when disposing of the container.

Have you ever experienced skin trouble after using contents exposed to the air like this?

They say the best way is to put it in an empty bottle and use it, but that's a hassle.