@Great Argus It's weird for me seeing a juvenile bird - off New Zealand coasts we really only see adults with brightly-coloured bills because the juveniles head directly east across the Pacific to South America after fledging. The all-dark bill just looks wrong. I wondered at first if this might be a Grey-headed Albatross Thalassarche chrysostoma but it's most likely a Salvin's Albatross T. salvini - apparently the most commonly seen mollymawk on pelagics off Peru.
@KevinB
I would guess so... Parque de las Leyendas keeps a lot of rescued animals, and if I'm not completely wrong, there was a sign in this particular enclosure talking about the origin of these animals. @Chlidonias
The institution lists this species as Phoebastria irrorata, but they don't really look like such. Agree with your guesses.
@David Matos Mendes yes it is 100% NOT a Waved Albatross. They have a completely different structure and colouration, and the bill is yellow even before the chick fledges (only in young chicks is it black).