I doubt that they will be the first couple to make such a private choice. Any children may wonder why no wedding pictures? It was one of my family’s rituals, finding the very large, very heavy Scrapbook filled with old photos, where we kids could see ancient black and white photos of my parents looking young, slender and all dressed up at their wedding reception.
One can have a wedding but not a government marriage
I have a high school classmate who divorced her U S. Navy husband and got almost ½ of his retirement pay.
She met another, they fell in love but did not marry because she would have lost her share of her existence retirement pay. I’m 100% for not having sex outside of marriage, but told her what she was doing was not unbiblical in her situation she and her friend stayed very loyal to each other until he passed away a few years ago.