Is there any harm of installing an improper print cartrige into a printer, if one does not know its code number; and just want to check it works or not?

If you install the wrong print cartridge it might not work becuase the inkjetsjets/printeads are wronly positioned, even if it is the same make.

It also could damage the cartridge holder, the cartridge and/or spray ink all over the inside of the computer. If you know the printer model, you can look up the cartridges that will fit.