You won't be able to go direct by sea on 6th April. It's too early. No-one wants to do that journey outside the holiday season. You might be able to do it via Syros on certain days but would probably have to overnight on Syros. Otherwise you'd have to go via Athens, either by flying or on ferries. Going by ferry would need an overnight stay.
I've just checked back at last year's schedule and it looks as though Flying Cat 4 made its first journey from Santorini to Mykonos on 6th April although that was on a Friday, but its next journey wasn't until the following Friday. However, I think that was just before Greek Easter which isn't until May this year. So this may be a possibility but until their schedule is published we won't know what date they are starting this year.
The provisional Flying Cat 4 schedule for the first few weeks of the seaon is now on GTP and Hellenic's web site - it doesn't start until April 27th this year.
That continues the usual pattern of FlyingCat 4 starting its season the weekend before Greek Easter.
Thanks Mikets. I hadn't realised that schedule was there yet. There's some odities like the Highspeed 5 finishing its morning journey in Tinos then starting its evening return journey in Mykonos :-), and Flying Cat 4 returning from Mykonos to Ios then Paros :-)Edited: 12:27 pm, February 24, 2013