Should be noted that WhatsApp is a texting app/service, and while you can transfer files via texting it's not a file transfer service. Also, to take full advantage of things like file transfers both sender and receiver need to using WhatsApp.
But getting back to the OP's query, you could just email her the photo. Or use whichever texting app you use, BUT it's important to keep in mind that if it's a higher res photo the file size might be relatively large and texting services often scale down attached media files. You're better off using email.
If the photos you're exchanging are more 'personal' than using email or texting transfers are generally not secure. In that case I highly recommend using Secureshare:
https://securesha.re/
It's limited to 10 MB file transfers but it uses secure encryption and after 7 days the file is automatically deleted off their servers, and/or you can set the number of days, up to 7, along with how many times it can be downloaded. So if you want to set a file so only your wife can access it just set it to one download and maybe just a couple of days.
If you have a lot of photos that the two of you exchange frequently, you might be better off setting up a service like Dropbox, or Google Photos, or Google Drive, or OneDrive. It's a really good idea to set up online backup/sync service anyway. Along with being able to share photos whenever you want and being able to access your photo archive from any phone or computer when you need to, it's important to back up things like your photos regardless.
