Bismillah ArRahman ArRaheem
Wa-Alaykum As Salaam
In order to pray your body needs to be pure.
In order to purify the organ you need flowing (kurr) water, or little water.
A moist napkin is not considered little water, but rather a moist napkin. So in order to pray, you will need to purify the body first.
However, having said all that, it is OK to "moisten napkin/bathroom tissue and wipe off the organ" and then " wash themselves with water at home afterwards and pray the salat".