Is it possible to train on bosses using weapons other than the dagger?

Solution 1:

New Answer: YES, and it's not difficult to do now.

Note: Look in the edit history to see the old answers.

Since Necrodancer's release, there is now an NPC available called the "Weapommaster" that will swap out your weapons for training. You need to buy him for 400 gold from Zone 2.

Solution 2:

The game now features a built-in way to do so. You can unlock the Swordmaster by buying a golden key in 2-2 for 400 gold (or at least, that's how I did it.)

From here you can bring any weapon to the training areas. Jump on one of the buttons to change the material of your current weapon.