I would want to desolder the USB, ethernet, mini-HDMI and audio ports.
Unless you have extensive professional experience with surface-mount soldering, forget about the micro-HDMI ports.
Everything else seems doable though.
As mentioned before, get several Pies, since you are bound to destroy several before you get the hang of it.
Maximize your chances with a good quality, variable temperature soldering iron. (With good rosin core leaded solder that was intended for circuit boards. Must be the "no clean" type!)
It's smart to use good lighting and a big adjustable magnifying glass. And a clamp of sorts to hold the Pi & wires still.
Buy some solid-core, thin insulated wire (to solder in the holes), and get started.
To desolder the large ports (like ethernet and usb), you can't easily melt all the connections at once for the plug to fall straight out. Instead you have to melt one side, rock (tilt) the connector a little bit, then melt the other side, rock the connector out a little bit more, and repeat as long as necessary.
After you desolder a connector, melt all those pcb pads again, one at a time, to stick in your wires.
On the other end of the wires, solder them all to the respective pins of your connectors.
Don't cross your wires. If you do, you may fry a usb device or router! It may be a good idea to test the continuity of all your connections before powering on your Pi.
This will take you days of hand-cramping work, having to start over every time you damage even one solder pad on the Pi.
You will probably have several minor burns on your fingers.
The equipment will cost you hundreds of dollars, and you'll end up with a pile of damaged of Pies at the end.
Last but not least: You may pull this one off, but don't even think about mass-producing such a thing. Quality control would be a nightmare.