So what you want to do is set the cold side of the peltier to the dewpoint so that you can collect the condensation and remove it from the cabinet.
You're going to attach some sort of aluminum plate/heat sink to each side of the peltier. The hot side will need a fan to turn on whenever the peltier is active. On the cold side you will also need a temperature probe of some type (e.g. LM35 or DS18B20) to measure the temperature of that side. Use the PID library to control the power on/off to the peltier (via relay or mosfet, preferably mosfet) to keep the dewpoint temperature of the cold side stable.
There's no PWM needed here, or putting it another way there's no reason why you'd need to switch the peltier on/off more than a couple times a second to keep a reasonably stable temperature.