I've been wearing neck knives daily for over 20 years. The only ones that ever threatened to come out were in poorly formed sheathes to begin with.
I've run with them, tackled and arrested folks in need of same and never had an issue.
I do not run paracord except through the holes in the sheath to keep the bead chain from clicking.
You want something, as BBI said, that will break away if you get hung up somehow, or someone tries to strangle you with the necklace.
Neck knives are awesome and a great piece of kit.