By "record" do you mean audio or midi or both? If you capture midi then you can "fix" any problems then play the midi back to your accordian and module whilst recording the resultant audio. You may need to to adjust the midi output settings of the accordian so as to capture all activity.

I think any recent Cakewalk is sufficiently powerful for you audio/midi recording needs although if you really want to mess about with audio files you may need something specific like SoundForge.