You can share your map publicly and provide your client with the URL. Make sure the 'Enable Public Measurement Tools' box is checked. They will see the same measurement tools you do on the Map's Detail page.
You could download the KMZ if you generated it and give that to them. Then they could do whatever measurements they need in Google Earth.
Aside from that they would likely have to either do some custom work or use the GeoTiff file in some GIS software to make measurements.