Controlling ancient 4 wire apartment buzzer (un-lock only)

I know this is almost 9 years old but I’m researching on doing something very similar with similar hardware and wanted to see if maybe you could offer some advice. I’m dealing with a Tek Tone IR207b (4 Wire 3 Button) intercom and I’m only looking at add the ability to “Buzz” someone in using a wireless remote.
The apartment building has separate video feed setup so when someone rings the apartment he just has to look at the video from lobby to see who it is and then be able to “buzz” them in without having to get up (He has MS so it’s not that easy to get up).
So I picked up UHPPOTE HBK-R03 433MHz 1-Channel RF Wireless Remote Control Switch, and I configured it for “Momentary” which means while he is pressing the unlock button on remote it’s the same as pressing the Door button on the intercom. My worry is that it’s not just as simple as splicing into the “door” wire, and I was hoping this internet is powered by 12VDC that I could tap into to power this device but not sure if it’s even possible, so I have a power supply I can use but it won’t be as clean as I hoped.
Thanks for advice or input you or anyone can offer me.
-Craig