Mykonos Crowds?

[TAC1582]

We are booked on a Cruise for next year (end of April/early May). I was checking the web sites that list what ships are in what ports for any given date and was glad to see that it looks like we will have all the port to ourselves, except for Mykonos where we will be sharing the port with a couple of large ships (we'll be on a smaller ship - capacity ~700). We've not cruised much before and never in the Mediterranean. Will this make the island unreasonably crowded or is it early enough in the season that crowds won't be so bad? How would this information affect the way we go about planning our day on shore?