They make a chisel handle that has different types of blades.
What you want is the half round one- X 155.
While you are messing around with it you might as well get a square one too.
Work with the grain, not against it.
I use a glove so I don't rub my soft little hands raw on the wood. Wouldn't want to chip my nails now would I
Do not work with the chisel on the last half inch of the barrel channel. Same same with the wood near the top of the barrel channel where a slip and goof up will show. Use your dowel for it so it is nice and smooth looking.