Hands Free Hairdryer stand.

It sounds like the kind of job that can be done by any generic movable arm type device, the same as the ones you'd put an iPad, or a light, or even a TV on (although one that strong would be overkill)

I'd try more generic search terms as there will be lots more available - if you find one that's good for something heavier than a hairdryer then it will likely handle that no trouble