Setup 2 pieces of aluminum (right angle cross section) on a wooden board, the one end a little wider than the untapered portion of your shaft, the other end the desired taper width. Put on sandpaper (100 grit works pretty well) with either glue or double sided tape. Chuck the shaft in your electric drill, run the drill at a medium speed and slowly feed it into the channel made by the 2 pieces of aluminum. It works pretty well.
I've done this with regular birch and I'm sure laminated will work too.
Jason