Is it permitted to use on Shabbos a flour sifter in order to sprinkle powdered sugar on cake?
It is permitted to use a flour sifter for this purpose. A flour sifter is a keli she-melachto le-issur, and it is therefore permitted to use it for permitted purposes.
Some authorities write that where there is a convenient alternative, it remains preferable to avoid using a keli she-melachto le-issur. However, in principle no prohibition is involved.
This assumes that the sifter is used for sprinkling alone, and not for separating lumps from the powdered sugar. To ensure this, one should make sure the sugar is fully powdered before beginning to sprinkle.