Hi daniel22222, I just had a look at the demo theme http://demo2.woothemes.com/artificer/
Using Chrome dev tools I removed the class you mentioned - it doesn't remove the button, but the button container loses its styles, so it floats over to the left.
I wouldn't edit the core files either, otherwise on updating the theme your changes would be overwritten. When you look at the function that generates the link though, is it wrapped in an _e() function? I presume so as that's a Woo theme, and I can't imagine that would slip through the net.
In which case you just need to figure out what's going on with your localisation. You mentioned you added your .mo file, and that changed the references elsewhere from 'cart' to 'basket', so the mo file was obviously being picked up, and your config language definition seems to be correct.
With the codestyling localisation plugin then, instead of using that to clear out the 'basket' references, simply overwrite them with the word 'cart'. If you clear them out they will revert to whatever is defined in the _e() function.
So to recap - ensure your mo file is in there, then give the plugin another go but overwrite them with the word 'cart' or whatever you want it to be.
Hope that helps.