Use Adafruit 16-Channel 12-bit PWM/Servo Shield to switch relays
That will work. Just make sure you are not using Servo part of the library, but only the PWM part, and set the duty cycle to 100%. The relay should still work, even if the duty cycle is slightly lower, as the magnetic field takes a bit of time to collapse. Just make sure you don't forget to add a (flyback) diode to the relay. 

Looking at the datasheet I think you need to use the following code

pwm.setPWMFreq(1000);//put this in setup()
...
// enable relay at channel 15
pwm.setPWM(15, 1, 0);
...
// disable relay at channel 15
pwm.setPWM(15, 1, 1);