Automating air purifier

Looking to see if anyone has experience with automating an air purifier. In my case I cannot use a simple automated plug because my particular unit has an push button electronic on/off switch, not a physical rocker switch. So if you leave the unit on and cut the power when the power is back on the unit defaults to off.

I like the unit I already have so I prefer not replace it, but I do not mind opening it up if its possible to re-wire the unit to always be on, then I could just use a z-wave plug. Below is the one I have currently.

Fibro relay. You can set it to pulls on and of