found on http://www.eisheschayil.com/private/questions/
where it says that the psakim are from Rabbi Webster of Yeshiva Emek Halacha
Question: Is one permitted to use babywipes on Shabbos?
Answer: There is a machlokes between various Poskim on this subject. If the wipe is paper then it really is no different than wiping a spill on Shabbos with a napkin. According to Rav Moshe Feinstein (Vol. 1) zt”l, there is no prohibition on squeezing a napkin since the intention is not to get the water, but rather to soak up the spill (although, water will come out of it). Rav Binyamin Silber Shlita, (in his Sefer Az Nidbiru) disagrees and holds that it is prohibited. (For deeper research into the topic, see Shallos Utishuvos Machza Eliyahu)
The Poskim of this generation are in dispute about babywipes. Some wipes are so saturated that liquid will be squeezed out at the slightest touch. In this case it would be prohibited (one must experiment with the different brands). If your type does not have alot of liquid (usually the first half to three-quarters of the box) than you may use it. In this case, one should refrain from using the last quarter of the box. Wipes that are medicated should preferably not be used since it is a Refuah and the substance on them could smear which is prohibited on Shabbos. If the baby has a rash and needs ointment one may dab it onto the area but not smear it, just cover it with the diaper and the diaper will do the smearing.