Maybe someone you know could take the yubikey device, attach a wire to it, then connect up a relay or something that could be controlled (using whatever interface you already have - I'm not that familiar with such medical devices) to activate the relay. When the switch contacts close, the other side of the relay could be connected to an earth-grounded point. That should activate the yubikey (I believe).
Note that the wire and relay and such will need to be shielded as well (to prevent stray capacitance - like somebody walking by or such - activating it). Coaxial cable like that used for oscilloscope leads would be great, and put the relay inside a metal box (and connect the shielding of the cable to the box).
Hmm - this is getting more complicated than I thought - but I think the basics are there. Here are some other links that might help as well:
http://playground.arduino.cc/Main/CapacitiveSensor (has a nice diagram/schematic of how these form a "circuit" for the microcontroller - this may or may not be what the yubikey uses)
A couple of PDF app notes from Texas Instruments on implementing capacitive sensing:
http://www.ti.com/lit/an/snoa952/snoa952.pdf
http://www.ti.com/lit/an/snoa926a/snoa926a.pdf
Good luck, and I hope this helps or leads somewhere for you!