This year where not a nidcheh can a girl going on a shidduch get a manicure during the 9 days?
Depending on the circumstances, if it is indeed needed for the shidduch, then it would be permitted.
Cutting nails during the week of Tisha B’av is controversial if it is permitted or not. The poskim say that it is permitted to wear Shabbos clothes for a date, and when needed to shower for the date. Cutting nails should not be worse then that. Additionally if a girl doesn’t have a manicure is not necessarily going to negatively effect her impression on the boy. Therefore it depends on the circumstances of each instance if it is indeed needed.