This isn't a complete answer because it doesn't address the wireless issue entirely but based on your comment about it being mounted on an adjustable arm something often used on machining equipment is something called a "scale" that is somewhat like a digital caliper. You can see a question I asked a while back DRO scales 4-pin connector identification to get a general idea of what they look like.
The OpenDRO project has full source code available that reads the values from the scales. From there you could read the scales on a microcontroller and transfer it via Bluetooth / WiFi. Depending on your level of experience that might be quite a bit of an undertaking but it might give you a pointer in the right direction.
I haven't used the RS-232 interface on OpenDRO myself (so you might want to check first with them it's possible) but presumably that could be used to transfer data over a wireless link that supports transparent operation. While somewhat costly that might be another possibility if you're only after a few systems.