The Mishnah Berurah (322:14) writes: If one is invited for a Shabbos meal, and he is embarrassed to go as he has some meat stuck in between his teeth, and he never prepared anything before Shabbos to clean out his teeth with, one may carry a splinter to clean out his teeth, if he has nothing else to use. The Sha’ar HaTziyun (12) adds in the name of the Pri Megodim that one is also allowed to snap a toothpick with his hand to clean his teeth, if he has no other option.
According to the L’Horas Nossan, one should be obligated to stay home, and not go to his friend in order to avoid violating the prohibition of muktzeh and making toothpicks on Shabbos. It is difficult to say the Mishnah Berurah is referring to one who has no food at home, and therefore, needs to accept the invitation and eat out. Tzorich iyun.
