the best tool for the job is a slim slotted bi-hex ring spanner of the correct BSF size. The Brooks tool is exactly that.
However the nosepiece shouldn't be able to rock from side to side over the shackle; there should be shoulders on the shackle that bear against the edges of the nosepiece. If these shoulders don't engage this usually means that the nosepiece has opened up somewhat. With a steel one, I'd happily knock it back into shape, but with a Ti one, you are playing with a material that has less ductility, so would have an increased risk of cracking.
cheers