Is one allowed to wear Shabbos Clothing on a date during the 9 days?
Yes one may wear shabbos clothes on a date during the nine days. The reason is that a date is considered a tzorech mitzva, and if the boy doesn’t look presentable it can have a negative effect on the outcome.
Shevet Halevi 9-131(4), Halichos Vhanhagos ( R’ S. Z. Auerbach zt”l) pg.9 ftnt. 44, Kol Hamisablim Aleha pg. 189.