For existing rides, you can go to the ride page on strava, and download the gpx - just click the spanner. You can't upload it to your own account, but you can upload it to another account, no problems. When you go back to your own ride, you will see it changed to "with two others" and their little avatars will be below yours.
Suggest you take a picture of their bikes as their avatars - nice for it to be personal, but still anonymous.