Your initiative and interest in family history is wonderful, and just knowing your grandfather had the sophistication to own an early wristwatch and a V&C at that, is impressive. However, there are many pitfalls with what you are considering IMHO. First and foremost, swapping cases and movements will result in a mismatched watch that cannot be considered genuine. Secondly, your case has been badly repaired and requires some restoration itself. Add the cost of service and restoration of any substitute movement you can find, hopefully with an intact dial and hands, otherwise good luck obtaining them too! It will be a difficult chore, but not impossible with patience and a great deal of knowledge. In the end, however, you will only have a faux momento as the watch won't be original or authentic .
May I suggest another route? If you have other items of personl property from your grandfather, such as a photograph, penknife, straight razor, etc., why not make a display box or cabinet vignette that includes this watch case and features the engraved back. I have something similar for my grandfather.