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 as neatly as possible.

I am throwing away the containers. There is often quite a bit left, so I use them multiple times and then discard the container. However, the problem is that I hear there is a risk of contamination because the cut end is exposed to the air.

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

I haven't had any major issues so far, but it looks unhygienic, so I am a bit concerned.

They say the best way is to transfer it to an empty bottle, but that's a hassle. Would it be better to just use the remaining contents once and throw them away?