Just wondering because the D-Pad controls are kind of bad and the touch screen option is pretty lame.

I would imagine mapping a controller on the touch screen using an emulator would not be allowed because the original hardware has no direct counterpart to this; am I correct?

Map the D-Pad options to an analogue stick on a controller or use the Wii U Virtual Console

Is easy, just map the D-Pad directions to a controller with analogue stick, works on a emulator, like Melon DS.

get a 3DS lol

Assuming you're talking about actually having full analog input, not just mapping d-pad to analog, the only way is with the toxinput mod which is not allowed in any runs. Almost all runners of this game just use d-pad since it allows for more precision, and in my incredibly unbiased opinion the game is fun regardless