Storing hex values as strings or integers?
I would recommend using the BINARY type; strings waste a lot of space, and integers require conversion.

http://dev.mysql.com/doc/refman/5.0/en/binary-varbinary.html 

For the other part: why do you need the associative table? If objects and fingerprints are 1 to 1, you could either store them directly in the object table, or just have single table with the id, fingerprint, and object id FK.