From the 2000 revival cast: Why Can't You Behave, Wunderbar, Too Darn Hot and Always True to You in My Fashion.
But...if you want a better overall KISS ME, KATE go with either the original Broadway cast (Masterworks Broadway) or the stereo remake (with most of the original cast) on Broadway Angel. Both are well sung and both have Alfred Drake.
Cast albums are NOT "soundtracks."
Live theatre does not use a "soundtrack." If it did, it wouldn't be live theatre!
I host a weekly one-hour radio program featuring cast album selections as well as songs by cabaret, jazz and theatre artists. The program, FRONT ROW CENTRE is heard Sundays 9 to 10 am and also Saturdays from 8 to 9 am (eastern times) on www.proudfm.com