He did it first when out with grandparents at a farm - it was a super-quiet one apparently.
Then I decided to make use of the time he and I spend at the local posh tennis club each week watching his brother have lessons, as it has a big disabled loo on its own corridor.
We donned his new lime green ear defenders (thank you so much for that recommendation) and spent the half hour on me setting off the handdryer while he counted its duration edging closer and closer (thank you so much to the person who pointed out that it's the unpredictability as much as the noise that gets him). Then he decided to do it himself!
I'm very proud of him.
I'm also very proud of myself because I genuinely didn't care about all the funny looks I was getting from the yummy mummies (and there were a lot!).
I shall recommend the tennis club to my local SN support group for hand-dryer desensitisation programmes .