I have only had one prop tossed off an engine, it was A four stroke that ended up needing A new needle valve assembly, I had fired it up, moved behind the plane and tried to run it up. Back fired and tosed the prop into my shop and right through the wing of A new Up-Roar that was getting maidened the next day. A very close call for me.
Just do everything Ken said and get rid of that wood prop. I have my students use Master Air Screws then I have them go over to APC. If the prop is tight and your engine isn't set too lean there should be no problem with A thrown prop.
Watching another old time pilot standing in front of his plane and reaching over the prop to twist the high end while he is operating the throttle stick too sends shivers down my spine. Fire it up and get behind it!!!