When you pick up your new passport, request your old passport (even if it has holes) back from the municipality. Bring both the old and the new passport with you on your trip to Peru. For the authorities there, it is sufficient that the passport number, name, and date of birth match, even if the passport has expired or has holes. So traveling with two passports to Peru works perfectly.
If you prefer to update your passport number to the new passport, you can provide it to us once free of charge.