Yeah I did that when the handle on my BS11 broke. It's not difficult to replace but you do need a bit of patience. The hardest part is taking the cone off the original handle I picked away at the wood a little at time until there we no wood left in the cone.
I wouldn't bother sanding down the handle myself as I wouldn't trust myself in doing it accurately enough. But if you feel you can, then by all means try that.