A few weeks after purchasing an Apple Watch, Wil Forrest smelled a problem.

Mr. Forrest, a manager at Freebirds World Burrito in Thousand Oaks, Calif., was cutting meat when the timer on his watch started buzzing and beeping. With his hands covered in meat juices, Mr. Forrest sniffed out a solution: He silenced the alarm with his nose.

“It...