You do not need the 3 shipping screws to replace the bed.
The wiki is very detailed, just follow it step-by-step. If you know which way to turn a screw, it will be very straightforward.
There are a lot of different types and sizes of screws. I found it helpful to print pictures with the screw locations marked, then glue the two letter-sized pictures to thin cereal box cardboard. Each screw was then inserted into the cardboard at the correct location as it was removed. This let me return each screw to the same exact spot. You might be able to use my X1C pictures with your P1S, but look over the wiki to verify, and make new ones if needed while you are waiting for the new bed to arrive