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Probably not since the sound is made by the tap dancer's shoes clicking off the surface, standard microphones (directional microphones with a cat's tail over it) should work better think of the surface of the floor as a percussion instrument and the shoes as drumsticks attaching one to a drum-skin wouldn't work well, but attaching it to the wooden body would. If you attached contact mics to the wall just above the floor they might work but if you want the sound re-created perfectly you're better off with conventional mics, probably two front and two rear for even sound distribution.
Hot glue is an electrical insulator, it wouldn't work well in place of solder. A soldering iron and solder cost under £10 or approx $10, not a big expense and you'll probably find yourself mending good earphones that broke at the jack from metal fatigue, a soldering iron saved an expensive computer headset multiple times as the wire kept getting pulled when I stood up if it was caught on something; you'll find that you end up mending items that you'd usually throw out and re-purchase, usually at a much higher price than the soldering iron and solder. Some flux; even though most soldering wire is coated in a bit of flux using soldering flux means you get better connections on some metals which seem to repel solder otherwise.