When you need to move BLOBs between databases (especially when DBs can't talk with each other), it needs a little bit more work, but it is still easy.
Necessary tools
SQL Developer
Oracle Instant Client with SQLLoader inside (file is called "sqlldr" and it's out of the box) - if you have SQLcl working, SQLLoader should work too.
Step 1 - Export BLOBS from source DB using SQL Developer "Cart"
Go to SQL Developer and use Cart to export objects containing BLOBs from your source database.
I prefer exporting files as a zip e.g. to /my_path/blobs.zip
Using Cart is well described in details by Jeff Smith here.
Step 2- Use SQL Loader to import BLOBs to target DB
Unzip the file created in step 1 to, e.g. /my_path/blobs
Ensure that you can connect to your target DB from the above location.
Use terminal and go to /my_path/blobs folder.
Review *.ctl file inside your folder - it shows what will happen if you run the script below.
sqlldr your_target_db_usr/password@your_db_tns_name CONTROL=BLOB_TABLE.ctl LOG=your_path_to_log_file/log.log BAD=your_path_to_error_log_file/err_log.bad skip=1
That's all.