I had Business Gold and Personal Platinum.

I upgraded my Business Gold to Business Platinum and downgraded my Personal Platinum because that new combination made more sense for me,
I got a pro-rated refund.

You are downgrading but the card is a small business card.
I would expect it to work the same way it did for me, but since yours is a small business card I would confirm with the customer service agent.
I would suggest saying that it is not because you do not like the Business Platinum card but that you have the benefits you care about covered with another Amex Platinum.