The Panasonic SV-as10 is a rather wierd looking 2MP camera and has shutter release buttons on both sides (one on the right hand side, and one on the left hand side of the back).
Might be what you want.
http://www.panasonic.co.uk/dsnap/svas10/index.htm
Panasonic list it's price at £250, so a bit above your price range.
http://www.bestcameras.co.uk have the older, as3 at £150 though. I don't know if this has the shutter release on both sides.