Although OTRCAT.com does not have recordings of every series listed below, the following is quick reference guide to old time radio show series, theme music title, and composer (when available).
Valiant Lady - " Estrellita (My Little Star)" - Manuel M. Ponce
Vaughn de Leath - " Red Sails In The Sunset" - Hugh Williams (m); Jimmy Kennedy (w)
Vaughn Monroe [orchestra shows] - Signature Theme on various shows: Racing With The Moon (1941) - Johnny Watson (m); Vaughn Monroe (w); Pauline Pope (w)