You can do whatever you want, but the spirit of the jam is to make things in the style of the limitations of the original Game Boy. Two things worth noting:
- It's a game jam, so it's a great place to try learning something new (for you, it might be how to do controller-navigated menus)
- Nobody is forcing you to stick within the rules. If you do have mouse controls, you'd likely just be sacrificing potential scores in the "Gameboy Soul" category.