Can mono be tranferred by sweat touching other peoples skin?

No. Mono can be spread through contact with saliva or secretions from the nose, throat, and other bodily orifices; but there is no credible evidence, to my knowledge, that it can be spread via sweat.

Related Questions

Can mono be tranferred by a sick person's sweat touching other people's skin?

No. There is no evidence that I'm aware of that mono can be transmitted via sweat. Blood, saliva, and other bodily fluids can do it, however.