Finding ship logs
This reference guide won't give you a direct answer to your question, but it may be helpful in searching for other resources.
The US National Archives and Records Administration (NARA) has a guide about the microfilm publication M2089, Selected German Documents from the Records
of the Naval Records Collection of the Office of Naval Records and Library,
On the four rolls of this microfilm publication, M2089, are reproduced
the contents of 34 logbooks and other bound volumes of original German
Navy and merchant marine records located among the Naval Records
Collection of the Office of Naval Records and Library, 1897–1917,
Record Group (RG) 45. The materials reprodued here constitute a part
of those original German documents approved for restitution to the
Bundesarchiv following the latter’s request and subsequent
negotiations with the National Archives and Records Administration
(NARA). For these German documents, microfilm publication M2089
represents the record copy retained by NARA.
The guide describes logbooks and other records from German ships, many from the age of steam. I don't expect you to find your grandfather mentioned by name in any of these materials. But this guide describes the nature of the material held by the archives, including the names of the different kinds of logbooks in German. You could use this background information for keyword searching, to look for other German ships' logs in other archives.
Finding Ship information
Another source of keywords for searches is Wikipedia's category page: Merchant Ships of Germany, which lists some of Wikipedia's articles on the individual ships, and other background articles. If you read German, check de.Wikipedia.org, too.
Contemporary reference books, such as Herbert B. Mason's Encyclopaedia of Ships and Shipping (1908) can be found on Google Books and other online libraries, and are good for finding background information.
Finding information about the port of Hamburg
The website The Maritime Heritage Project, focuses on the maritime history of San Francisco, but check their Research Sites page for links to International Maritime Museums and World Seaports for Germany. Scroll down the Germany page to find the section on the history of Hamburg as a seaport.
Possible record sources for Merchant seamen
You may have difficulty finding records for your grandfather because of the way the records were created and collected.
At Find My Past (subscription required), the description for the database Merchant Navy Seamen says:
There are more than 2.6 million Merchant Navy Seamen records, which we
are publishing in partnership with The National Archives. The Merchant
Navy Seamen records comprise two main sections:
Merchant Navy Seamen 1835-1857: records of individual seamen that the central government created to monitor a potential reserve of
sailors for the Royal Navy. Over 1.6 million records are available to
view between these dates.
Merchant Navy Seamen 1918-1941: records of index cards that the
Registrar General of Shipping and Seaman used between the two world
wars to produce a centralised index to merchant seamen serving on
British merchant navy vessels. There are 998,838 records available to
search between these dates.
The records are split into two very distinct sections / timeframes
because in 1857 the Board of Trade abandoned the Seamen's register,
deeming the agreements and crew lists enough to meet the department's
needs. This means that no register of ordinary seamen's service was
kept between 1858-1913.
However, you might find something in England & Wales Merchant Navy Crew Lists 1861-1913:
The records include many born throughout the United Kingdom, Ireland
and further abroad. Furthermore, the records include the names of over
700 Lascars from Asia and the Indian subcontinent.
If you want to learn more about the history of the ship companies and the ships involved, try the website The Ships List. Here are some routes that were used in the time period you are looking for, which I found by searching the site for Chile:
There's a great deal of information on the site, but it can be fun to explore.