Since no one has responded to this, I thought I would at least add my thoughts.
You can use this keypad without diodes but there will be some problems if you push 2 or more buttons at the same time. True this isn’t a normal use of the keypad but finger checks do happen. To protect against having 2 of the CMOS output ports shorted together when 2 or more keys are push simultaneously, I would just put a 220 ohm resistor in series with each of the output lines going to the 74hc595 chip. This will protect the hardware.