It depends on the game. Some official Wii-to-WiiU conversions (e.g. Xenoblade) can use the Gamepad as a Classic Controller. You may be able to create icons on your Home Menu that launch with this option using TeconMoon's injector. Some games that use the Wiimote sideways like a NES controller can be patched to use Classic Controller. But if you want to play most Wii games with other controllers (e.g. Dual Shock with motion controls), you will need to use the Dolphin emulator on PC rather than a real Wii.
Just wanted to play Mario Galaxy 1 & 2. Loaded the game and it wanted me to pair the wii remotes