Stop my old iPhone from backing up
(a) iTunes named backups (on your hard drive) using the UDID (Unique Device Identifier) of successfully connected iOS devices. So it's erroneous to state that a backup of a 3 GS will overwrite a backup of another device since each device has a unique UDID.

(b) iTunes 10.5.1 doesn't provide option to not back up. However, you could uncheck the "Open iTunes when this iPhone is connected" which then allows you to connect your iPhone to iTunes without triggering a backup.