This is a link to check on ferry schedules: http://www.gtp.gr/RoutesForm.asp. Using it you will find out the options for all your ferry rides.
I did an experiment for the Athens to Santorini part. All ferries seem to leave from Piraeus very early in the morning. At least all of them seem to run on Sunday.
The 2 that leave at 07:00 are fast, passenger only Catamarans (get there in about 4-5 hours), but if it's rough, they may go slower and you may not want to be on them, and if it's too rough, they won't go. The 07:35 is a car and passenger ferry, but it takes about 8 hours.
There is a public bus, X96, that goes all the way from the Athens airport to Piraeus. This is a link to it: http://athensairportbus.com/en/X96-bus-from-airport-to-piraeus-port.htm. It takes about 1.5 hours, depending on the traffic. You would have to leave very early indeed to get to the ferry on time. You might want to contact your hotel about that.
Of course, for many times the price, you could take a taxi which will get you there a lot faster, especially on a Sunday morning very early. This is a little Rome2rio search I did for the transportation options from the Athens airport to Piraeus: http://www.rome2rio.com/s/Athens-Airport-ATH-Greece/Piraeus. Considering your tight time schedule, I'd choose the taxi.
Now, here's the link to Aegean for flights: http://en.aegeanair.com/. If you can get a flight at this late date at almost any price I would take it vs. that long or bumpy ferry ride, particularly since you will be at the airport anyway.
Be advised that Santorini Airport (http://www.santoriniairport.com/) is on the opposite side of the island from the caldera. I don't think it would be a reasonable walk from there to your hotel. You will have to take a bus or a taxi to or near to your hotel. If your hotel is one on the caldera with a beautiful view, you may find yourself going down and up lots, and I mean lots, of stairs.
Santorini Ferry Port (http://www.santorini-port.com/) is a few kilometers from Fira (next door to Imerovigli), so you would also have to take a bus or a taxi into town.
By now you may have guessed that the hardest part about traveling in Greece (except maybe that you can't flush TP down the toilet) is the logistics. Assuming that you plan to arrive in Athens in less than 2 weeks, you need to get busy with these schedules and at least be informed on what's possible.