Dismissal or resignation - FCA register

I'm under 30 and I've been at my current job for 3 years. I had a chat with the CEO a few days ago and he dismissed me. I'm registered with the FCA (CF30) and I'm getting calls from the COO that he has to notify the FCA before the last working day of my departure (it's my understanding that you have 7 business days to do this after departure). As a personal favour, he can put "resignation" on the FCA form. He claims that if he puts dismissal, I'll have to explain why I was dismissed on my next job and 10 years down the line I might have problems because of this. I suggested "redundancy" because I haven't used my CF30 capacity in over 2 years. He doesn't want redundancy because he can't hire a replacement for 3 months.

Is this really going to show on a background check? If it does, is it really that bad? I've no problem explaining a dismissal to a future employer. My job doesn't require CF30, they just wanted to have more CF30 registered people.