If this is still relevant...
Friday afternoons are difficult because the Jewish Sabbath begins at around 4:30 PM these days.
However, a quick (Hebrew) search found the following phone number for an Akko-Haifa sherut operator:
Moniyot Kavie Hagalil ("Galil Lines Taxis"): +972.4.8664422
You can also try english dot b144 dot co dot il, and search for taxis in Akko.
Finally, you could try to arrange for a return taxi/sherut ride by asking the operators when you get off the ship in Haifa. You might have to deal with them not being too happy about you not wanting a ride to Akko, though...
Enjoy your visit!
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