If this is a feature request then it should be moved to the forum of the same name. Do you want me to do this?
I agree it could be nice to be able to run the CRC test withoout the overhead of the entire game and its dependencies.
I'm wondering about why you need a CRC check in the specific use case of automating the download of mods from the mod database, though, is it actually needed there?
The 'cksum' command you find on Linux systems as part of GNU coreutils is one which is specified by the POSIX standard and this one is indeed not compatible to the one the game uses (nor those of BSD, System V, Windows CRC32), since its checksumming algorithm differs.