If I have peanut shells on the table on Shabbos, and they are Muktzeh, what can I do to dispose of them when there is no tablecloth?
I can but quote the Sh'miras Shabas K'hilchasah and hope I'm doing so correctly. CYLOR for a practical ruling.
20:26 (in a chapter on Shabas): Shells, seeds, and bones that aren't human food and are also unfit for animals — or even fit as animal feed but there aren't animals around — are muktze and one may not move them, and see 22:36 and 22:42, below. But one can take such shells, seeds, and bones when emitting them from the mouth and place them on the plate.
(Someone cracking seeds shouldn't hold the shells in his hand so as to throw them later, but throw them immediately he cracks them or place them on the plate.)
If some of the meat is left on the shell, seed, or bone, or something edible is in the seed..., even if he has no intent to eat it, or bones with marrow in them, are not muktze and one may move them. See 20:27, below. [End of 20:26.]
20:27: Shells, seeds, and bones fit as human food, or even fit only as animal feed but such an animal is around, like orange peels..., may be moved, even if he threw them into the garbage or street on Shabas. But if he threw them there before Shabas, they may not be moved.... [End of 20:27.]
21:2: Although we said in 20:27 that there's no muktze rule on Shabas on shells and bones fit for animal feed, on yom tov one should be stringent and practice the muktze rule even on such shells and bones if the shells were removed from the fruit or the bones from the meat on yom tov, so they are forbidden to move, unless he needs the place the shells and bones are occupying if they're on a dining table, as below, 21:3, or if they're bothering someone where they are, as below, 22:42.... [End of 21:2.]
22:36: Thus, bones, shells, and the like, although unfit for animal feed, which are on the table: If he needs the clean table, dragging them by means of a knife or (dry) rag is permitted, as is shaking the whole tablecloth. Likewise, sweeping the floor of a room he's using is permitted, although he'll drag a muktze object while sweeping. See 23:1-2, below.
(If he considers the waste on the table disgusting, he can remove it even by hand, according to the rule of g'raf shel rei, below, 22:42. That's permitted even when he doesn't need the clean table.)
On yom tov removing these bones and shells is permitted even by hand, if they're on the table and he needs the table to be clean for the yom tov meal, as above, 21:3. [End of 22:36.]