You wil find such a reader:
Buy one of the PocketBook models with buttons, e.g. the Touch Lux 3, and install brucelee's
CoolReader3 fork. In CoolReader, you can set the action that should be performed when you tap on one of the tap zones (i.e. parts of the screen). One of the options you have is 'no action'. So, if you set all tap zones to 'no action' you have what you want.