You may need pull up resistors on each of the 74HC165 inputs to ensure a known state when the reed switches are open (unless they are SPDT). But as resistors are 0.1pence a shot, cost isn't much of an issue, and space shouldn't be too bad.
Having said that you would still need a pullup resistor on each input of the 74HC165 for the other method as well for the same reason.