If one urinates a few drops on the toilet seat on Shabbos, is he permitted to wipe off the urine with a detached toilet paper, or would this be forbidden because urine is muktzeh?
The שולחן ערוך 208:34 allow moving disgusting things such as excrement and allows it if it is in an area that people live in. A bathroom is part of such areas.
כל דבר מטונף כגון רעי וקיא וצואה בין של אדם בין של תרנגולים וכיוצא בהם אם היו בחצר שיושבים בה מותר להוציאם לאשפה או לבה"כ ואפי' בלא כלי ואם היו בחצר שאינו דר שם אסור להוציאם ואם ירא מפני התינוק שלא יתלכלך בה מותר לכפות עליה כלי: 34. Anything filthy like excrement, vomit and dirt etc., whether from humans or chickens or the like, if it is present in the yard where people gather, it is permitted to be taken out to the garbage or to the lavatory, even without the aid of a utensil. If it is found in a yard that is not used for living purposes, it is forbidden to remove it from there. However, if one is afraid a child might get dirty from it, one is permitted to cover it with a utensil.
The question is hardly whether the urine is muktseh; as the other response mentioned, it is allowed to move that which is filthy because of the "kavod bnei adam" that is involved, and there are several laws regarding the manner in which this itself is possible.
The question involves a few other halachas, namely sechita (wringing) and telisha (detaching). In what manner is it permissible to detach the paper with which you intend to clean the seat? And then assuming you have in your hand with what to clean, you would have to do it in a way that is permissible. You should be careful to wipe with something dry (Rashi's view regarding borer being applied to objects other than food, and how it would apply to a wet wipe used to clean the floor and so on - I believe it was in שיט in Shulchan Aruch), and then when cleaning it, you should hold the paper carefully so as not to accidentally "wring out" any of the liquid that builds up on the paper, even a drop, since this would be a serious violation of "sechita".