Do accounting not get a record of everything you purchase on the corporate card and require an explanation (or else repayment)?

Yeah. Keyboards, headphones, mice, monitors, desk chairs purchased for software engineers... Pretty self explanatory.

Here's how that'd go in the last two companies I worked for: Purchase declined. Not valid under T&E policy. Please follow IT acquisition policy for computer equipment and real estate acquisition policy for furniture. Card payment is due by xx/xx to reimburse for invalid expense.

That sounds a little too... bureaucratic?

Anyways, final approver should be somewhere between you and the CTO.