You don't need a 5V switching reg to run the PS2 then, but depending on what screen you want to use it might be a good idea to get one anyway. Not all screens will run off 7.4v input, but almost all can be 5v modded. The Texas Instruments PTH08080 is a good switching reg for this purpose, paired with 2x 100uf 15v electrolytic capacitors to clean voltage ripple (the diagram only shows a cap on the input line, but you should use one on the output line too for safety) and a 330ohm 1% resistor to set the voltage. Here's a diagram for wiring one up.
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I don't think Amazon carries them, not any legit ones anyway, but Digikey and Mouser definitely do. You may find them designated as PTH08080WAH or PTH08080WAD, these are the same regulators, just one has pre-soldered pin legs on the bottom that we always remove anyway for space saving.