No use fixing green wood, let it dry first.
You bow tip doesn't need to be any thicker than 1/2" so you have plenty to work with and get the crack out.
I bent a hickory static lately that cracked, I filed out the crack and had pretty thin tips so I added a a 1/8" thick strip of osage to the back to reinforce the bend, this also keeps the bend from pulling out over time.
As you can see the hickory gets pretty thin in the bend, this is where my osage strip is the thickest.