You can apply for the business card while holding the existing cards, but since the rule change last year you can't get another personal until you cancel the existing ones. The business and personal cards are counted separately. Even with a legit business, some suggest for the business card just applying as a Sole Proprietor with your SSN and business name exactly the same as you name for simplicity. In an odd twist, people with actual businesses seem to have a harder/longer time getting a Chase business card than those of us with "businesses". If you're not in a rush you can apply with all your legit s-corp paperwork, but Chase might want the documentation and such before approval.
As for the credit score, it shouldn't take much of a hit if you're going to be replacing that credit line with a new card anyway. You can also move some of your existing CL to other Chase cards before closing it. (keeping in mind it's easier to get approval if your Chase CL to listed income ratio is less than 50%, usually) If it's an age of accounts concern, just know that your closed accounts remain on your report for up to 10 years and continue to influence your score, so it's not usually as dramatic of a hit as people think.
Even better! My $45 still plays hide and seek as I try to decide what I want to buy to use it up. Their site is glitchy as I'll put something eligible in the cart with something that wasn't and I won't get it to apply, so I remove the ineligible item, refresh or update and still nothing. Empty the whole cart, start with just the eligible item and then it'll show up again. It's been bizarre. I'm half tempted to stock up on a year's supply of Mac & Cheese and have done with it.