Deanna,
as you have no exact date of depature from Hamburg, you have to look into all 103 newspapers of the Allgemeine Auswanderungs-Zeitung for the years 1863 and 1864 to find the exact date of depature of this ships. See this link:
http://zs.thulb.uni-jena.de/receive/jportal_jpjournal_000000...Attached is some info I found by chance in this newspaper
Klaus