Do they even need it, or can they just snap their claws and switch gender?

Probably not, it likely wouldn't do much of anything either due to them being sexually monomorphic, or due to dimorphic traits being genetic, as opposed to being hormonal.

Do dragons have either?

Totally depends on what sort of chemical signaling they evolved. Some definitely would, but others might not. If they don't Estrogen and Testosterone could either do nothing for them, or be pretty toxic.

For Elder Scrolls dragons like the one posted here, they don't really have different genders or sexes because they're made by a god splitting pieces of their soul or something similar. They probably could change their expression in various magical ways, but who really knows ¯\_(ツ)_/¯

They don't need hrt, they have magic spells and shit.

Some people out there deny the validity of us dergs unfortunately.

Identity labels are about the destination.

Destination. Straight trans people usually think they're gay before realizing they're trans.

The final product, most of the time.

Whoa that's crazy, what was it like ruling Ethiopia for almost 20 years?

Reminds me of Analog Closed Captions that analog TV, VHS, and many DVDs have.

That's clearly Alduin

So you didn't played Skyrim.