By far the easiest way to play Mario Kart Arcade GP 2 is on a soft-modded Wii. The Triforce arcade board which Mario Kart Arcade GP 2 ran on was based on Nintendo's GameCube hardware which was also the basis of the Wii's hardware so being pretty much its native platform the game runs perfectly.
Soft-modding your Wii is perfectly legal and relatively easy to do, a good resource for this can be found at https://sites.google.com/site/completesg/
The best software to use to play Mario Kart Arcade GP 2 on your soft-modded Wii is Nintendont which also supports other Triforce Arcade games including F-Zero AX, Mario Kart Arcade GP 1 & 2 & Virtua Striker 4.
The latest version of Nintendont can be downloaded from https://github.com/FIX94/Nintendont
Enjoy!
GAME CONTROLS Gas: R trigger Brake: L trigger Throw: A Insert Coin: Z