You can play older CD Dos games on DosBoxWii. I would suggest first working out how to get in working, through DosBox, on your PC. When you have done that, you use the same commands you used to mount your PC CDrom, by either adding them in your Wii's DosBox Config file or by simply typing them in manually after DosBoxWii as started,
I haven't used DosBox for a while, but I remember it being pretty simple to mount a CD Drive (something like : mount e g: as cdrom. Presuming my CD drive on my PC is g: and I want it to be known as drive E: in DosBox) Its something like that, though obviously you replace g: with whatever DosBoxWii Identifies your Wii drive as. You then just navigate to the starting executable, ie./ CMD e: , followed by run.exe or whatever, you get the idea.
To find the exact format for the 'mount' command, concerning CD Drives (or even Cue/Bin files from SD or HDD if supported on the Wii version) go to the DosBox home page, the full list of commands is there somewhere, or just search google for 'how to mount cd drive in dosbox', that'll also give you the answer I am guessing.
Definately find out how to do it in regular dosbox first, then just adapt it to the Wii's parameters (or hardware).
P.S. you could do what you already did, by copying the fikes to USB, and then just replace the original executable with a NOCD Patch version (google is your friend).
Good Luck.