For this you will need a file manager installed on your phone. Try Folders beta.
Now all you need to do is:
1. Navigate to the folder where your video is.
2. Cut or Copy the video.
3. Paste it in the WhatsApp folder under the Pictures directory.
4. Now go to WhatsApp, tap the attach button, select albums swipe to Videos.
5. There you will find your video.
6. Enjoy sending videos.
Now all you need to do is:
1. Navigate to the folder where your video is.
2. Cut or Copy the video.
3. Paste it in the WhatsApp folder under the Pictures directory.
4. Now go to WhatsApp, tap the attach button, select albums swipe to Videos.
5. There you will find your video.
6. Enjoy sending videos.