When you view the slideshow in Photos you will see an "Export" button the upper right corner of the window.
Exporting will write a video file of the slideshow to a folder on your Mac.
Click "Export" and select a format for the final video. For a good quality select "High Definition". Send the finished video to the recipient. If it has a very large file size, put it into your Dropbox or somewhere, where the person can download it or copy it to a USB stick and send the stick as a letter. You can also burn the file onto a CD and send the CD. If the video file is small ,send it by mail.