Choosing decoupling cap for M74HC595B1R shift register
You definitely should have decoupling capacitance on your board. I would recommend a 100 nF ceramic or similar per IC.

You also should have bulk decoupling capacitance distributed across the circuit, as befits the load on the gate outputs and the distance to the source power supply. For myself, I would put a 10 uF capacitor for every 3..5 ICs. I would also have a 47 uF capacitor by the power supply, be it local regulator or input connector.

As an aside, will you have a series resistor between each IC output and its loading FET gate? Otherwise, on an IC output rising edge, it's trying to charge the gate capacitance which first appears as an instantaneous short and dips your rail. The resistor limits the gate charging current and gives your IC a better life.