There could be influenza virus on the pump handle. It can survive for hours on surfaces.
I have never had influenza.
If you were to touch a surface that was damp with infected bodily fluid from an Ebola victim, you wouldn’t need to rub your eyes to catch the disease. The virus can enter through microscopic cuts in the skin. I don’t know about you, but I have tons of tiny cuts.
I work with many microbiologists. I am a biochemist. I think we have a good understanding of virus behavior.
An emergency kit would include hand lotion? I have grandkids - any other suggestions if it start spreading?