Your trip sounds great! I actually did the same trip (circumnavigating Long Island) 4 years ago with my first boat a 25' Mark 25 which is similar to a C&C25. I was 22 at the time and not too experienced and most of the time I was single handling but it was one of the best experiences of my entire life and I will remember it forever. Now that I have a much bigger and capable boat I would think twice about doing it again in that little 25' footer (especially the part where my girlfriend and I were punching into 30knts of wind coming back from Block Island headed to Greenport in 6-8 foot chop and having to constantly bail out the cockpit with a baseball hat since the scuppers where getting swamped!)
Anyway we did do Shinnecock inlet and while what everybody else mentioned is absolutely correct, if the conditions are good and you know the tides then you will be fine and it is not as bad. I would check the weather before you leave and make alternate plans that if you can time the tide right and the weather is good, enter the inlet and stay the night as it really is a beautiful little bay - BUT if it is not conducive then have a backup which would most likely just be sailing overnight. However one thing to keep in mind which no one else did mention is that if the weather is not too great, sailing on a dark night close to shore with fishing boats and other junk in the water can also be dangerous - As dangerous as navigating a tricky inlet? I don't know and obviously there are many factors to take into consideration while making that decision to see what option is best.
So I don't mean to ramble on. I do agree with everyone else that it is a very tricky inlet especially in poor conditions, but it is not un-doable and can actually be a peace of cake if the conditions are good. The upside is you won't wear yourself out sailing overnight and you get to experience a beautiful bay.
If you do stay, there is a marina just west of the inlet with a great (but kind of expensive) outdoor seafood restaurant. They let you dock for free if you stay just for dinner. For the overnight portion we motored further back in the bay and anchored in a little cove just south of the Shinnecock canel. It was such a nice night having a great dinner, watching all the boats come and go out the inlet and then having a peacefull night of solitude on the hook in a stunningly pretty back bay.
I used to keep the little 25' on the Great South Bay so I also did the Fire Island and Jones inlet and for the around the Island trip I actually went on the inside out to Shinnecock through the bays since I only had 3ft draft (and barely made it) but unfortunatly that way would be too shallow for you.
After that we did a straight shot out to Block - stayed a few days there then went to Greenport, Sag Harbor, Mystic, Port Jeff, Stony Brook Harbor, Northport Harbor, down Hell Gate and around Manhattan into Liberty Landing Marina on the Jersey Side - then out the narrows back into the Atlantic for a long day back to Fire Island inlet and into the Great South Bay back to Patchogue where I kept the boat at that time.
Now I have a 32' Morgan which I sail out of Mt. Sinai on the North Shore of Long Island. If you want, hit me up in July when you go on the cruise. My friend's and I have a number of moorings in Mt. Sinai harbor, Port Jefferson Harbor and Smithtown (stony brook harbor) so if your interested in staying in one of those locations I could probably hook you up with one of them so you don't have to pay.
Again sorry for the long rambling post but as I said before I had an amazing time on this trip and wish you the best on yours!