Are green branches ok for a young rabbit?

[Calico]

I have a young bunny and wanted to give him some twigs from one of our apple trees to chew on. I trimmed off a handful of thin branches, but they're all still fresh and green inside. Are these safe for a young rabbit, or do I need to find older, dried wood? I know they're not supposed to have greens or vegetables yet, not sure if the same applied to branches? I also scraped the buds off of the branches I cut.

I ordered some willow toys online for him, so those are on their way, but in the meantime I thought it would be nice if he could have the apple branches. We have several trees that are badly in need of pruning anyway