Michael Johnson, a great popular songwriter and performer, has used a classical guitar for his work throughout his career and has always used a strap. And he doesn't play cheap classicals either - his current instrument is a Kohno. Here's his setup:
Kohno classical guitar: “Professional – R” built in 1991
Pickup: Baggs LB-6-X
D.I.: "LR Baggs Para-Acoustic D.I."
Strings: D'Addario LP Composites Normal Tension, with a Savarez Alliance High Tesion (Blue Card) for the third string.
Here are some
concert photos on his website.
If you ever get a chance to see him perform, take that chance.