74hc165 inverting pins 15 and 2, does it work?
If I am interpreting your question correctly, you are confusing people with the word "inverted" where you meant "swapped".

From the datasheet, pin 2 and pin 15 feed the same OR gate that then feed the edge-trigger clock of the internal registers. So they are functionally equivalent. And it is confirmed in the "function table" and they even share the same setup and hold time from "Dynamic characteristics". The specific datasheet I am looking at is from NXP.