First of all, even in peak season Turkey in general and Hisarönü in particular will not be crowded in any respect. (Göçek is an exception..)
First catamaran or monohull; I would rather go with the mono first and with the cat later.
You have three options for the nights:
-mooring (no problem anywhere..)
-restaurant jetties (for popular restaurants, such as Octopus in Söğüt, the one in Dirsek and Sardunya in Selimiye, etc, you'd better come a bit early than usual) will never have a problem of finding a spot for mooring
or in marinas
even with much larger boats.
-marina. The only option is Mart marina in Orhaniye (Keçibükü) you will find as much space as you want but they are extremely pricey. 40 ft cat for a night would pay 100 + a night..
Hisarönü is a very good spot for sailing; always a bit of wind and no large swells. Meltemi (north westerly, more westerly as you go inside the bay) sets up a bit late than usual the last 5-7 years, so May could stii be a bit unpredictable. There are many bays protected from Meltemi and it blows usually around 12-20 kts.
Otherwise, in May you can still have some southerly/south easterly which can be stronger. In this case, the places like Orhaniye and Bozburun still offers perfect protection.
You can PM me if you need more info.