It isnt going to hole well like that. I have heard of native americans sticking the head in a branch and letting the tree grow around it but this seems highly impractical. You can dish the inside on one end of the wood out into kinda a cone shape to fit the celt in. Hope this helps

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Make sure it's sharp And keep your hands, feet, head etc out of the way of both the tree and the axe

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no problem 

Make sure the celt does not touch the sides of the hole.  If it touches anything other than just the top and bottom of the handle, as you chop, it will wedge it deeper and split the handle.  When you chop with it, hit at almost a 90 degree angle, then hit several inches above.  You need to hit more than the diameter of the tree apart.  When your chips come out, they will be humming and will fly a great distance.  James Parker told me those little tidbits, I wish he had told me before I broke about six handles.  If you can find one, a copper busse bar makes a really great celt.  Bill

Hallo there Dan!
I'm not very much into handling stone axes, for that I have made just one (but I'm preparing the second, I have crafted the axe and am now preparing the handle.... a set of picture will soon appear here  ).
But I've seen many of these axes, and I've come to a conclusion: the "conic hole" is the best way to handle it, but I suggest you not to pierce the whole handle.
I mean, "dig" the handle, but leave some wood intact, so that the axe will stay there, when you use it.
I'm sorry for my poor English, I don't know if you have understood, but as I said I'm preparing a handle and I'll post a picture that will explain exactly what I mean!
Greetings,
Mauro.