Unicycles aren’t supposed to have handlebars… and they look kind of silly, anyway!
Unicycles are composed of a wheel (which includes the tire, tube, rim, spokes, hub and axle), the cranks, pedals, frame, seatpost, seatpost clamp, and saddle - that’s it.
Some may say that brakes are ok… and I can kind of see that line of reasoning (though I don’t totally agree with it) since brakes don’t alter the basic concept of a unicycle that nearly everyone on the planet visualizes when thinking of a unicycle - namely one wheel, no handlebars!
So if you’re riding with handlebars you really should just refer to your ride as a one-wheeled vehicle, since it’s really no longer a unicycle.