Is altering your Wii's internal clock the only way to trick the game that it's still daytime or can you do it within the game?
You can change the clock within the game, but then the game will "know" that you are cheating. If you change the Wii clock, the game will not realize you are cheating unless you happen to set the clock backwards past the last time you played the game. So if you were to play, say, December 20th at 3PM, as long as you don't set the clock back before that time then you would be fine.
There are only a couple of consequences for time traveling, if the game knows you did it that is. Turnip prices will plummet to 40-50 bells, red turnips will rot, and Redd's Shop will be closed for the entire week.
Also, I don't know if this matters to you, but any time spent playing the game when the Wii is not set to the correct time and date will not be recorded in the records of the Nintendo Channel.