I have done this in the past in the same way you basically describe. I scanned the original faceplate and used the image to create vector artwork in AutoCAD. A test printout on plain paper allowed precise measurements to be made for correcting any scale errors.
Then I either printed the final image on high resolution flat paper or glossy photo paper intended for inkjet printers and used spray adhesive to attach it to the original metal faceplate. The slight added thickness of the paper has never been an issue.
The results in both cases looked as good or better than the original faceplate but had the advantage of color printing if neccessary.
@Max...re printing on CDS...great idea....you could get an old CD, carefully cut out part of the CD the same size as the meter face, put the meter face in the hole thus created, attach it with stickytape on the back of the CD and faceplate, and print. You might have to pad the faceplate up a bit - it probably would not be as thick as the CD.
If the background of the scale is still nice and white then you can get some correction fluid like "wite out" or "Snopaque" and cover just the numbers and letters but not the scale markings. Then use Letraset dry-transfer lettering to replace the letters and digits. You can get it on eBay and at many craft stores in the scrapbooking section.
If you decide to re-print the scale markings and everything, you might try getting an inkjet printer that will print on CD's. You could easily modify it to accept the meter scales.