Ignore the previous post. Here is the updated solution.
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A little tricky but doable without uploading videos to any cloud, drive etc.
In iPhoto, create an event and change the title to - say, "Transfer-iPhone". Import all content, photos, videos in iPhoto, and drag into Transfer-iPhone Event.
Go to itunes, connect your device, in RHS under Settings, go to Photos section,
1. Check "Sync Photos"
2. Select "Selected albums, events..."
3. IMP Check "Include Videos"
In events section, select Transfer-iPhone. Sync.
Now videos will be available in the videos section when you're sharing via whatsapp. And Photos, well they are not directly available, you can always select them ("they will be available in your albums - under "Events"), and tap on "Add to", create a new album, or add to an existing album. This album will be available while sharing on whatsapp.
P.S.:
1. It might take a little while before a newly created event appears in iTunes, weird, but happened with me. I quit both iPhoto and iTunes and launched them again.
2. If you don't have iPhoto installed, or don't want to use iPhoto, you can use the drop down after "Sync Photos" and choose the folder under "pictures" from there. You'll have to copy your content in a folder created in the "Pictures" Folder. But again, the photos will not be directly available. Workaround is same, select and add to a new or existing album.
3. I've been using latest version of iTunes on Mavericks, and iOS 8. Hopefully things will work in similar manner on iOS 7 too.