At first, I was going to say "go for 3", but it seems you have already been through enough heartache trying to gain acceptance from your wife as a BL. If I knew the "details" that Blackstone mentioned below I might change my opinion, but as it stands now, it seems to me to be perfectly normal to give a birthday present to a boy who values you as a friend. It will make his day just that much brighter.

You don't need to tell your wife, I think. If she finds out and says something about it, you might mention that there is nothing abnormal or inappropriate about a birthday present.

As for giving it to him in public vs. private: in public, he takes the gift and gives you a hug. In private, he takes the gift and gives you a hug. I see no difference, but again, I don't know the details.

Do what is best for all if you can,
Hikaru