Umbrella shaft clamp?

Not sure if something like this even exists, but I figured I'd ask.

My Profoto D1's use a friction mount for an umbrella shaft, which is fine most of the time, but when you're outside and there's a little wind it can pretty easily pull the umbrella out of the mount.

I'm wondering if a small clamp exists that I can tighten on to the umbrella shaft so it can't slide out.

Here's a photo of the back of the light so you get an idea. I'm hoping to clamp it on the backside of the light shown here (obviously I would have to push the umbrella through a bit more).

Seems to me that a standard(very small) C-clamp would get the job done, if you can't find something that is purpose-made.

You could also drill through the shaft, and insert a cotter pin/nail/stick. On the even-lower tech side, would a hose clamp or even rubber band work on the very end?