Congratulations on your marriage!
It is a wonderful spot for a honeymoon.
I am a bit biased though.
You are correct that Lakes Region Conservation Trust has possession of a small amount of the island, near the top I believe. As you stated though, there is no public access or docking to get there.
There are lots owned by the Rattlesnake Island Association, which can be used by us owners. (Not well marked.) If you are renting on the island that means you may hike here. No problem. There is a trail that is marked and well traveled. Hiking boots are a good idea.
What part of the island are you going to be on? Wolfeboro seems to be the closest for shopping by boat at IGA and there is a bakery in town, The Yum, Yum Shop. If you are talking by car, that depends on where you have it.
If you would like to talk more, feel free to e-mail me. Island living requires some planning, but it is the best. Good luck!