I am unable to do it right now, as I know nobody else with a working Wii, but to put your mind at ease, I'll show the information straight from page 23 of Monster Hunter Tri manual:
Exporting Character Data
It's fun to play at a friend's house, so when you do,make sure to save your character data to your Wii Remote and bring it with you. Here's how.
1: Select "Export Character Data" Choose "Arena Play" from the top menu, and then select "Export Character Data" from the game mode selection screen.
2:Choose Select File Firet, select the file you want to export.
3:Select Character Data Next, choose the character data you want to export.
4:Choose the Wii Remote to Save to Data can only be saved to Player 1's Wii Remote. If the Wii Remote contains other game data, be careful, because it will be overwritten. When the save is complete, all you have to do is load the data to another Wii system.
Make sure there are no Miis in the Wii Remote as number 4 specifies. --- Neopolitan Ice Cream, official flavor of the indecisive.
I just found out. The character transfer only works under ROM (read only memory) conditions. It's solely used for the arena and is not transmitted to the Wii memory at all. I'm afraid that when you play the game on your home Wii, you have to start from scratch. What a bummer. --- Neopolitan Ice Cream, official flavor of the indecisive.