No, in Hook's eyes. Henry is apart of Milah, and most of all, Bae. You can't just get rid of a third generation like it was Gods way of telling him, this is the ONLY WAY to get rid of your enemy. The man who killed his love, Henrys grandma, his hand, Henry's step-grandpa. It'll be so cruel and I dont think, any of us wouldn't approve, esp. Emma. If, they're gonna make CaptainSwan happen in Neverland, then I don't think he'd risk the chances of getting even with Rumple once and for all, by the many failed attempts of trying to kill Rumple. Would he really kill the son of the boy, that couldve been his actual son, then his grandson?! No... There.
I don't think so. Hook looked at Bae as his own, he loved Bae. With Henry being Milah's grandson Hook would never try to harm him. Beside with the way he offered Emma his ship and his help once he learned of Henry being kidnapped I highly doubt he would do anything other then save and protect Henry.
I don't think Hook has any interest in killing Henry. In fact I believe that Henry could be more in more danger from his Grandfather than from Hook. I could be wrong, but just get the sense that if Rumpel gets back to his 'Dark One' frame of mind, he could consider killing Henry, as he did in 'Lacey'
That said, I very, very much would love to see (once he's been rescued of course) some kind of moment with Hook and Henry discussing Milah. Kind of 'Milah would have been so proud of you Henry' and Henry enquiring about his Grandmother and Hook telling him that she was beautiful, brave etc. Would like to see this because I would have a natural curiosity about the Grandma I could never meet, especially when not only do I know my paternal Grandfather, my maternal Grandparents are young enough to be my parents...