When it comes to biomedical equipment, I would not suggest opening up and tapping into any of the wires, even if you are sure it's just the display wires. I would look for another way. Does the piece of equipment have any port on it at all? If so (or if there is a simliar model with one) I would consult with the manufacturer for drivers or at least a programming guide in order to write your own.
If none of this helps, there is one more solution. IMAQ Vision from Labview. NI has a great package for image recognition. It is very jitter resistant so if the image moves around (you say a protable meter) it will still give you reliable feedback. I can picture some sort of clip on device that would clip over the front of the meter like a cover. This cover would have a
small digital camera mounted so it aims directly at the display. A mechanical engineer could design this knowing little more than the outside dimesions of the meter, the dimesion down to the center of the display and the focal distance of the camera.
I hope this is of some help. Good luck
Jared