I wanted to play NSMBW for the first (kinda) time, in anticipation of the upcoming Super Mario Wonder. I did not feel like shaking the Wii remote though, and looked up other control options for actual hardware. (emulator can work around this pretty easy)

It looked like from some googling, there was an ocarina cheat code to use with wii USB loaders (on your own backed up disc) that would allow one to use a classic controller.
 

Enable Classic Controller [Thomas83Lin]

C21EB5B8 00000020
38210050 7C0802A6
80BA0060 48000041
809A0000 7CA52378
90BA0000 80BA0064
4800002D 809A0004
7CA52378 90BA0004
80BA0068 48000019
809A0008 7CA52378
90BA0008 7C0803A6
4E800020 70A40200  --> possible R button line
2C040000 4182000C
3CC07FC0 90DA0010
38C00000 70A40800
2C040000 41820008
60C68000 70A40020 --> possible Y button line
2C040000 41820008
60C60200 70A40040  --> possible B button line
2C040000 41820008
60C60100 70A40001
2C040000 41820008
60C60002 70A40002
2C040000 41820008
60C60008 70A48000
2C040000 41820008
60C60004 70A44000
2C040000 41820008
60C60001 70A40400
2C040000 41820008
60C60010 70A41000
2C040000 41820008
60C61000 7CC53378
60000000 00000000
041EAE30 39800000
041EAE34 91840000
04019EE0 38000000
040B3B30 38000000
2076DBA8 8804A2DC
0476DBA8 38000000
2076DBE9 8804A2DC
0476DBE8 38000000
E0000000 80008000

You'll notice some comments about "possible" button mappings.

The controller mapping is Y run, B jump, and R shake. This is fine for the original Classic Controller, but I didn't want to use that controller since the analog shoulder buttons aren't that comfy to use.

Ideally I would want to use a Classic Controller Pro, and use ZR for shake since nintendo changed that to the "main" shoulder button (a weird change that persists to today on Switch Pro Controller)

There was some information online about remapping the buttons in another game, DKCR, with another Classic Controller Code by Thomas83Lin, that made sense but didn't seem completely applicable, from reddit.

The responder mentioned "Classic Controller Button Activator = 28200F0A 0000XXXX." , but the first line in the cheat "28200F0A" wasn't in the DKCR nor NSMBW cheat.

This thread does also link an article about the cheat code however, ( http://www.pixlbit.com/news?action=showNewsArticle&newsArticleId=1037 ) which contains comments showing what button binds go with each line of code.

Classic Controller Support (v2)
C24A5F70 00000020
38210050 7C0802A6
80B50060 48000041
80950000 7CA52378
90B50000 80B50064
4800002D 80950004
7CA52378 90B50004
80B50068 48000019
80950008 7CA52378
90B50008 7C0803A6
4E800020 70A40020 --> button (in this case Y) which triggers the shake
2C040000 4182000C
38C0012D B0D50186
38C00000 70A40800
2C040000 41820008
60C68000 70A40200 --> button (in this case R) which simulates a 1 press
2C040000 41820008
60C60200 70A40040 --> button (in this case B) which simulates a 2 press
2C040000 41820008
60C60100 70A40001
2C040000 41820008
60C60002 70A40002
2C040000 41820008
60C60008 70A48000
2C040000 41820008
60C60004 70A44000
2C040000 41820008
60C60001 70A40400
2C040000 41820008
60C60010 70A41000
2C040000 41820008
60C61000 7CC53378
60000000 00000000
04389B90 38A00000
0438710C 28000009

I searched for similar lines in the NSBMW cheat, which led me to find "70A40200" was the R button bind in the cheat code. I substituted the ZR button activator, giving me "70A40004", and the following code.

New Super Mario Bros Wii
Enable Classic Controller ZR Mod [Thomas83Lin + Firestarw]
C21EB5B8 00000020
38210050 7C0802A6
80BA0060 48000041
809A0000 7CA52378
90BA0000 80BA0064
4800002D 809A0004
7CA52378 90BA0004
80BA0068 48000019
809A0008 7CA52378
90BA0008 7C0803A6
4E800020 70A40004  --> ZR button = shake
2C040000 4182000C
3CC07FC0 90DA0010
38C00000 70A40800
2C040000 41820008
60C68000 70A40020 --> Y button = Run
2C040000 41820008
60C60200 70A40040  --> B button = Jump
2C040000 41820008
60C60100 70A40001
2C040000 41820008
60C60002 70A40002
2C040000 41820008
60C60008 70A48000
2C040000 41820008
60C60004 70A44000
2C040000 41820008
60C60001 70A40400
2C040000 41820008
60C60010 70A41000
2C040000 41820008
60C61000 7CC53378
60000000 00000000
041EAE30 39800000
041EAE34 91840000
04019EE0 38000000
040B3B30 38000000
2076DBA8 8804A2DC
0476DBA8 38000000
2076DBE9 8804A2DC
0476DBE8 38000000
E0000000 80008000

If you want to change any binds yourself, here's the button activator codes from the reddit thread:

XXXX Values:
0001: Up DPAD.
0002: Left DPAD.
4000: Down DPAD.
8000: Right DPAD.
1000: Minus (Select)
0800: Home.
0400: Plus (Start)
0008: X.
0020: Y.
0040: B.
0010: A.
2000: L.
0080: ZL.
0200: R.
0004: ZR.

Hope this helps anyone wanting to play NSMBW on Wii or WiiU. Alternatively you could play in emulator with a Switch Pro controller or some other 2D controller with motion controls, and a good controller experience while also being able to use the tilt controls for a few levels, since this classic controller code can't implement that.