I'm not sure what the song playing on the radio is, but the tango you are thinking of is "Por Una Cabeza", written by Carlos Gardel. During the early 1990s, the piece was used in "Scent of a Woman", this film, and in "True Lies" a year later.
Although it is performed in the film by a small group, a very close approximation can be found on an album called The Tango Project, available at https://www.amazon.com/exec/obidos/ASIN/B000005IX3/qid=1119804456/sr=2-1/ref=pd_bbs_b_2_1/104-8539186-0968758. The rest of the album is really good as well, but if you prefer, the piece (and one more tango) is available on the soundtrack album for "Scent of a Woman" as well.
Hope this helps,