How do I modify a refrigerator water line to add a shut off valve and flexible pipe?
The solution is fairly simple. Cut the copper tubing about a foot from the floor and install an inline valve. Use a compression coupler type valve and run the remainder with plastic tubing. Food grade 1/4"  plastic tubing will fit well on a 1/4" compression or graduated/clamp fitting. These fitting are available at building box stores or RV stores.