You should be able to point the installer at Time Machine during setup. This will make the OS you have on there now largely irrelevant. Just ensure your drive is USB attached, and hold option ⌥ down as you boot, select your installer CD for Snow Leopard, and do it from there.
The following Support Article should help
Restoring your entire system from a backup
If you are restoring a backup made by a Mac to the same Mac
With your backup drive connected, start up your Mac from the Lion
recovery partition (Command-R at startup) or Mac OS X v10.6
installation disc. Then use the "Restore From Time Machine Backup"
Note: If "You can't restore this backup because it was created by a
different model of Mac" appears when restoring a backup that was made
on a different Mac, follow the onscreen instructions.