Cathay Pacific Transfers on separate PNR?
They'll through-check your bag so no need to clear immigration and customs at HKG to recheck. They may be able to print your onward BP in PER, or you can self-print at online checkin.
I don't have personal experience, but I get the impression CX is quite good at rebooking missed connections even on separate tickets. Linking the PNRs might help ground staff see where you're coming from.