No you don't need a shock spring on a DP.
I agree, unless its illegal in your area not to have one. An in-line swivel is a good idea on any trap but certainly NOT mandatory to hold coons. I haven't added one to my DP's for years, coons will twist out if it stops swiveling but unless something like the springs getting hooked over your stake happens or maybe in a tree root, you'll be ok. I've never had one twist out in grass, it still moves enough. If you're getting losses in DPs with toes still in the trap, likely you had it stabilized too hard in the ground so they twisted and injured it before they pulled it free of the ground. Then they lunge and tear free.