Can you determine what the reference to Hannover was? The
reason I ask this is there was/is the city of Hannover and
was the Kingdom of Hannover. In the area I grew up in
Iowa, all of the references to Hannover was to the Kingdom
of Hannover.
It would be great to be able to restrict your research to just the city of Hannover, but there are a lot of towns in the Kingdom of Hannover, and those changed often.
Since you are beginning your research on your family history, a quick tip. The degree of success you will have will largely depend on how much preliminary work you do close to home. If you can document your most immediate ancestors (parents and grandparents) as thoroughly as possible, it makes pushing things back further considerably easier. If not, you'll be striking out rather blindly, with far less "ammunition" to work with. When it comes to "crossing the waters", it is pretty much imperative that you know the village, town or city in Germany in which the family lived. "Hannover" rarely cuts it, since it was a kingdom consisting of countless towns and villages far beyond its city limits.
Make sure to gather up every available record - births, deaths, marriages, obituaries, cemetery, etc. - you can regarding your more immediate family members on the Peruvian end. These will often provide additional clues as to the family background and particulars. If there are elders still around, interview them for more insights on the family past. Look through any surviving family memorabilia for old letters and documents. You may well have some luck on the list here - anything is possible - but more often success comes from using a basic building block approach. Start with what you know, gather any available local records for analysis, and then work backwards - methodically.