How should I alter my PISO shift register circuit so that it works with 3.3v instead of 5v?
The pullup/pulldown resistors for the buttons can take almost any value, limited only by power supply current capacity (1-10 ohm) and noise resistances (hundreds of kilohms).

So in the referenced schematics, you can put any resistor between 1K and 500K, and it will work, no matter what the power supply voltage is - 3.3 or 5V. I like using 4.7K resistors because I have a big box of them.

For more complex cases (I2C, etc..) the rules may be more complicated, but buttons/switches really do not care.