Is the wetness coming out of the anus - which has no smell and is accompanied by excessive sweating - impure and necessitates ghusl or changing clothes before the time for prayer?

If the wetness you find is continuous and issues from the private parts, then it is excused, and there is no need to wash it from the body or clothing. Prayer performed with it is valid. This is the Maliki school of thought, which offers ease. However, if you are not certain that it issued from the private parts, then consider it pure sweat, which does not require washing, because the default state is purity until certainty of impurity is achieved.