This is actually a real question that can potentially involve 2 issurim- 1) getting a garment wet can be an issue of cleaning (melaben) and 2) of squeezing (sechita, the mealacha of dosh), if the garment gets wet enough to squeeze. As far as I know the Halacha, and it pays to ask your Rov of course, wiping with a disposable napkin is ok, or something like a rag that is designated for spills. You would still have to be careful not to squeeze-meaning avoid getting it soaking wet- whether it is the cloth or your skirt that got soaked by sitting in the puddle.
There is a story I heard once about a Rav who got out of bed in the morning and stepped into the negel vassar water with his socks on. Since he was afraid if he stepped down or pulled off the sock he would squeeze, he sat like that the whole shabbos.