There is a small harbour 6 miles from there called Garlieston (Wigtown Bay side) that i have seen small boats tied up in. Never used it so cannot say more, but was there not a trawler lost from Whithorn about three years ago. That would suggest some sort of facility is at the Isle itself. Check tourist information, they might help.
In fact check this out:
follow link - how to get there...by sea...harbour master phone number and all the detail you need inc cost of berth overnight...ain't google wonderful!