The HORI Split Pad Compact Nintendo Switch Controller is designed for handheld mode, and you can get one for $31.99 shipped, today only, originally $49.99. In addition programmable rear trigger buttons, there’s also Turbo functions to set buttons to rapid input at 5, 12, or 20 button presses per second. Product page.
Remember the old NES / SNES gamepads with the Turbo button? The HORI Split Pad Compact also has a Turbo Hold function to set the button to continually activate Turbo without having to actually hold the button down. It’s officially licensed by Nintendo and compatible with both the original Switch as well as the Switch OLED model. For those who prefer GameCube-style controllers, there’s the Retroflag Handheld.