Revealing mistake: When Sam pops open the cabinet with the wire he will later cut, you can see that the wire was cut and glued together again. When Sam cuts the wire some time later, it's in perfect condition. The taping was probably done in reverse order.
Plot hole: Someone as careful and controlling as Timo would never force anyone into working for him, for exactly this reason.
Chosen answer: It might not actually have one, in which case, he'd have to go down into the club and use theirs. As for showering, going to his mother's house or a gym membership would take care of that.
Captain Defenestrator