I have a few different bench hooks here Sylvain, from a small one used to support the far end of long pieces, to one made just for cutting with the japanese saws to a properly beefy shooting board sort of arrangement; but none were of use here because you needed to hold a piece an inch wide vertically while cutting across its width to make the handle. You might cut two from the same piece and later rip it in half to seperate them; that extra width would give you something to clamp in the vice. Or just use a carvers vice like this one:

The small jaws let you clamp smaller pieces well. But then I’d have to make it and then I’d have to find a place to keep it and it’s getting crowded in here 😀