you can use it. my grandpa converted his old tractor to 12 volts and left the 6 volt starter. As far as I know he still is.
I have been using a six volt starter on the flat head straight six in my 48 Plymouth on twelve volts for four years now without any problems.
The beauty is that it will spin over at mach 9, it will start better than it ever has. It works fine.
Got a 6 volt starter on the flatty with a 12 volt system and for the last 5 years been spinning the hell out of it and to date no problems
If the engine has good compression and is tuned up right, it should pretty much start like turning on a light, so the starter shouldn't have to run long enough to get it hot. Grinding on the starter until you get the starter hot and run the battery down will kill any starter whether it is 6 or 12 volts. Keep it tuned up so it isn't hard to start, and you won't have any trouble with a 6V starter on 12V.
Used 6v starters on my Beetles that were 12v, spun over like crazy, never fried one. I put a 6v on my Fergeson tractor that I converted to 12v. Snapped the starter housing a couple times. I just kept brazing it up.
You will probably want to change the solenoid and maybe the bendix. The 6 V starter should last altight but the bendix working twice as fast as it chould might put some wear and tear on the gears.