I have opted to replace this section with a piece of beech as I had some offcuts in the workshop.
Step 1: Turning
Rough the blank round using a roughing gouge.
Once round measure the handle and mark the length on the wood.
Then using a pair of callipers transfer the end size of the old handle onto your blank using a parting tool.
Then reset your callipers to the size of the middle of the handle and size the centre the same way.
Using either a spindle gouge or a skew chisel blend a smooth curve from the middle to each end.
Once you are happy with the shape reduce the waste wood on either side with a parting tool to as small as comfortable.
Then sand the wood with 120,240,320 grit sand paper and then seal with sanding sealer.
Once the sealer had dried apply wax and buff.
Step 2: Removal and Fitting
The original handle was fitted with a bar through it and the ends rounded over. To remove this I cut to the bar with a wood saw, then through the bar with a hacksaw and back to the wood saw to finish.
To refit the handle I decided to drill and fit M6 t-nuts into the handle and then use pan head machine screws to secure it. I would recommend applying something like thread locker or epoxy.
I did it this way as I didn't have anything suitable to fix all the way through the handle.
Handle replaced and the shovel is back ready for use.