The buttons you pictured are indeed for a HAPP door and they only fit a HAPP door. Coinco, Coin Controls, and Happ are all different.
Coinco buttons don't fit Coin Controls doors. Coin Controls are metric standard. At one time when Coin Controls was at their height they had buttons available in different colors. Not so today. The major coin door manufacturers, Coinco (Coin Acceptors, Inc.) and Coin Controls along with changer/bill acceptor manufacturer, Ardac, were all bought out by Money Controls. They promptly closed out the amusement and coin door product lines of these companies.