I find an appropriate style and play. If they want to hear the original, they can hire the REAL guy, or play MP3s, tapes, records, etc.
I love to play this way.... Just choose a style that the right timbre, and play along it... And thats why its a pitty that many of todays styles are almost somgspecific
However some songs, like for example Vangeliis conquest of paradise have such a specific timbre, that a songstyle comes in handy...