Is PID and EC linked to TID and SID in any way?

Okay so i wanted to make a traded eggs SV match the hatchers TSV so that I'd hatch a shiny pokemon that looked like it was traded as an egg. Since pkhex only generates shinies for the breeder's TSV and not the hatcher's I figured I'd just substitute the hatcher's TID and SID in, reroll the encryption constant and PID and then change the TID and SID back to the breeder's. Will this still be fully legal? I can't find any mention of the PID and EC being affected by the TID and SID but I just want some confirmation

Is PID and EC linked to TID and SID in any way?

EC, no, PID, yes. The PID generates a PSV/ESV, a number that if it matches with the TSV (determined from the TID/SID), the egg will hatch shiny. Yes what you're asking is legal, those aspects have no baring in legality. Met info and moves are the biggest factors for legality anyways.