A simple option is to use chord diagram images rather than trying to copy them as text. Most chord sites let you right click the diagram and save it as an image, then you can just insert that image into your Word document.
Another easy method is to use plain text chord boxes from sites that support ASCII diagrams, then adjust the font in Word to a monospace font like Courier New so everything lines up properly.
If you are creating a lot of charts, programs like ChordPro or Guitar Pro can also export clean chord diagrams that paste nicely into Word or PDF.