The Rama, z"l, mentions that one may not do any lowly or menial tasks in the Sukkah. The Mishnah Berurah explains that this includes washing pots and pans, but adds that washing cups would be permitted.
The Ben Ish Hai's opinion is somewhat different. He comments that one may not wash utensils in the Sukkah, even if it is only one utensil, as is mentioned by the Ahronim. He adds, however, that those very small cups that some use for coffee (such as for Turkish coffee), may be washed, provided it is only one cup.
The Mishnah Berurah does not appear to make any distinction regarding the size of cup and would also appear to be more flexible in terms of how many cups may be washed. The Ben Ish Hai appears to hold that no more than one cup may be washed and that it has to be a very small one. Obviously, washing all utensils outside the Sukkah, alleviates all problems.
(See Rama, 639:1. Mishnah Berurah, ibid., 9. Ben Ish Hai, 1st year, Haazinu, Oth 9)
Sukkoth, Sukkot, Succos, Succot, Sukkah, Succah, washing vessels in the Sukkah