What is trust:
It is the tranquility of the soul of the one who trusts his heart's reliance on the one in whom he trusted to do what is good and right for him in the matter of the trust according to his ability and knowledge of what is for his good. But what lies at the root of his trust and gives rise to it, without which there can be no trust, is his sure confidence that the one he trusts will keep his word and do what he promised and that he has in mind to benefit him even in what he did not commit himself to or undertake to do out of pure grace and kindness. pg364
Hilchot Shabbat
The concern with using baby wipes on Shabbos or Yom Tov is that the Melacha of Squeezing will be violated. If the wipe can be used without Squeezing, then it may be used on Shabbos. A baby wipe that is slightly moist and gently dabbed into the diaper area would be an example of permissible use on Shabbos.