cabotage is finished here.
but to get permission to run regular ferry routes, that is a different story. needs power.
still i believe the only foreign flagged vessel running regular ferry routes in Greece is the Incat Fast Ferry SPEEDRUNNER I which is UK flag but it is a joint venture between the UK company Sea Containers and Greeks.
problem with this request is that 4 hours Mykonos to Athens is only going to be possible on Fast Ferry, Yacht or Hydrofoil. With hydrofoil though it would be better to go by plane i guess, its similarly not so fun.
RM ELEGANT will do 100 passengers for Day trip I believe. If you can afford any of the solas yachts though. TURAMA is another choice.
Otherwise in the more budget sector there are vessels for day cruise like PEGASUS, MANTALENA, ALCYONIS if you check the following site. I am not sure if they will be able to do the voyage in 4 hours though.
http://www.yachting-mediterranean.com/
SEADREAM I and II also but they may have schedule already.