In addition to the dimensions of the CD-8 grille shell being different from the CM model, the CD-8 insert has moveable louvers to allow an increase and decrease of airflow when the engine is running. The CM model has fixed louvers.
Earlier I read a comment regarding using the CD-8 4 spd transmission as a form of overdrive, the four speed is a 3 spd with an extra compound low gear, great for steep hills at slow speed and driving in a parade, otherwise fairly useless. The rear end has 4.10 gears and really needs some form of overdrive. I know others have asked about the 1937-39 Mopar 6 cyl overdrives, I have several of them and they do not fit in a CD-8, everything on the CD-8, including the transmission is significantly larger. I have not located an Airflow 8 cyl overdrive transmission, so, I do not know if they fit.