Look on line for original paint colors for a 69 Barracuda. That stuff is posted. Once you have it narrowed down visit an automotive paint store that has been around for a while and they may have a catalog of Chrysler paint samples and formulas of colors.
I have jumped online and narrowed it down to the 2 I called out. I am hoping someone may know of another location the paint code may be stamped on the body. Otherwise, I will have to do as you suggested.