The phrase "privilege of skinship" somehow makes me want to cringe. It has this effect in English, but when translated into Japanese it has the double-effect of confusing me while at the same time making me want to cringe. Firstly, it is a vague, contrived word that somehow has made it into the Japanese lexicon. Two people who are so obviously "love-love" as you are convinced you are, do not require advanced written notice in order to hold hands. You are turning a natural expression of affection into something unnatural. It is as if, for the avoidance of doubt, you are telegraphing your desire to touch her, which is not only unromantic, it is amazingly creepy. It would be one thing to say (verbally) to your lady friend that "it would be a privilege to hold your hand", but announcing in writing that you think its time for you to enjoy this privilege is the opposite of romance. And, if you are saying the privilege is for both of you, you are presuming too much. It is an oddly puritanical sentiment that would be creepy even if you were both Puritans. And why do you need to take the relationship to the "next level" in order to speak honestly to each other? It makes it sound as though you have not been honest with her up until this point. Or worse, it makes it sound as though you are bargaining; that you can only be honest with her if she agrees to share the "privilege of skinship" with you.
If you are trying to charm your lady friend, I think it would be better to do so face to face. And, I wouldn't assume that she will be moved by your effort at translation. It might cause confusion. It might have the opposite effect from what you intended.