The original mouth piece attachment that comes with the hairdryer is almost purposefully bad with poor direction of air flow. It also is only held in place with 3 click in tabs that fails almost comically easily.
I created a thinner and more directed nozzle that prints easy in ASA or other heat resistant material like PAHT-CF.
After temperature testing the hairdryer extensively I determined that the hairdryer very rarely breaks 95C and almost never 100C degrees.
Printing in ASA with a temperature resistance of up to 106C is sufficient but if you want to be absolutely certain of the functionality you can print in nylon like PA or PAHT.
I suggest printing standing on the nozzle and ironing the surface that's going to be up against the hairdryer. This will ensure the best fit. The 5 tabs that keep the attachment in place can easily be printed with no support. They barely extend a lines width over the side of the print.
I recommend printing between 101-102% scaling due to shrinkage but you may way to measure your hairdryer with calipers to ensure the correct fit as I am sure the tolerances in the production of the hairdryer aren't the greatest. Printing at 101.5% worked for me.