I know I'm a little late on this topic, but if I had to guess anything, it's probably more likely the input-lag on your TV (Assuming it's a flat screen).
Most LCD TVs have a considerable amount of 'input-lag' meaning that the time between the TV receiving input from your console and the actual time it outputs is noticeable. People who watch TV or movies wouldn't notice this, but gamers notice right away because they're impacting the input on the TV by actually controlling the game, so that time difference is critical. This was never an issue with the old CRT TVs because they never had any input lag.
If you're interested, read about it on Wikipedia:
http://en.wikipedia.org/wiki/Display_lagThe only reason you may be noticing this on the virtual console compared to other Wii games is because most games nowadays are designed with the input-lag in mind and aren't as time-critical as older games are. I notice it most on the original Super Mario Bros for NES.
If you still think it's the classic controller, have you tried using a GameCube controller? (Assuming you have the original model Wii with GameCube compatibility)