I did something like this with a PS3 back in the old days with an Uno rev.1 and a DualShock 3. I took the DS3 apart, found the traces that interfaced with the buttons and broke them out, which was pretty hard - the traces were carbon-coated like remote control contacts because the button pads were on a flexible PCB, so I scraped off enough carbon until I could solder to them, then I soldered tiny 30AWG wires onto each - there were something like 20 of them (the D-pad, L1 and L2 had a common, the shape buttons, R1 and R2 had a common then the start, select and PS buttons had a common too). After that I soldered everything up to opto-isolators. This was before I knew really anything about electronics, it was difficult, clunky and not great but it did what I wanted, at least.
If I were to do it now, I'd have a USB-capable board like a Leonardo plugged into the PS4 and then some sort of IR, RF or Bluetooth device hooked up to that to send button presses, but I haven't tried making a fake DualShock 4 with a Leonardo yet. I wouldn't want to hack the PS4 itself to break out the capacitive sensors on it, though I'm sure that would be easy enough if you have an oscilloscope to see what signal the sensor sends down the wire because it might not be a simple voltage. Then again, it might be.
There's also something called GIMX which I think can be used to interface any device to make it appear like a game controller, so maybe there's something there you can look into.