I have been doing some reading on Arbors in general and realise that my attempt was quite crude. I have since produced a better version of an arbor for holding the cutter.

With the constant interrupted cut I decided I had room to fit a M3 screw off-centre so I have also included this in the new arbor. It makes it look more cluttered but in terms of functionality, at least there is no chance of the cutter slipping.