That's how I would do it. I used to do it with black-pigmented epoxy, after gluing into holes in the timber, an arc of stainless steel wire (say 0.5 mm) bridging the gap, and maybe a couple of other lateral ones, for reinforcing. I don't know if this was really necessary, but felt I needed to do this to guarantee the job, considering that the timber may be saturated with grease in this area.