just don't. if it says only for residents, that means exactly that. doing otherwise is asking for trouble. if you don't want to pay that fare there are other airlines with lower fares –unless it is a destination served only by LATAM–.
to paraphrase liam neeson: they will look for you, they will find you, and they will charge you the 100% difference.
i'm not sure of when they will notice it, if when you do the booking or when they see a ID number different than the peruvian ID or the foreigner permit, but they will know about you.