Hi David
There will be small code modification needed. Look at the file components/com_eventbooking/view/cart/tmpl/default.php and you should be able to see the button code and remove it
And if you only have one event, maybe you should disable shopping cart. Go to Events Booking -> Configuration, set Activate Shopping Cart config option to No, then it should work as expected without having to edit code
Regards,
Tuan