Women must certainly chant the twelve names of Perumal and Piratti while applying Srichurnam and Thiruman. My preceptor had instructed to chant the appropriate names at the relevant place one applies the Thiruman. For example, after applying Thiruman in the forehead we have to fold our palms in supplication and chant Keshavaya NamaH, Sriyai NamaH.
Though it is stated women should also apply Namam in twelve places like men and also it is impractical for women to apply them in certain areas like fore arms, chest, neck instead they can chant the relevant names of Perumal and Piratti by folding their hands in reverence.