What would be the most convenient tool/method for moving blob data
from one Oracle database to another? I have a table containing 55
columns with a column of blob data type and others of varchar2, number
and date types. There are roughly 45000 records in the table. The task
is to copy all the data from this table to another table residing in
different database. Both database are Oracle 8i running on UNIX.

Use Oracle's own export and import utilities.  Export from one and
into the other.  go to otn.oracle.com and click on documentation.

You may want to use thirdt party tool like FastReader wich
specializing in extract  / load data from Oracle. FastReader from
WisdomForce (http://www.wisdomforce.com) allows quickly to extract
large Oracle tables into flat files and generates control files for
sqlldr*. FastReader is supporting blob types.

Forgot to mention that WisdomForce FastReader does support Oracle 8i on UNIX.

How about DataBaselink ?

insert target_tab (select  ... from source_tab@link);