I found using a seam ripper that has one prong protected by a plastic bead very helpful.
Most seams have a narrow strip of material "seam tape" sewn over them, which is easier to remove if you snip a few threads to get started, then place the beaded prong under the seam tape, and pull the seam tape towards the seam ripper while under tension. Once this is removed, use a similar technique to pull the seam you are trying to cut towards the seam ripper while you keep tension on the material on both sides of the seam, exposing the thread you want to cut without snagging the nylon material. I hold the ripper between my thumb and index finger to direct it, and prop the handle against my chest while pulling the material apart and towards me.
Both processes are much easier for those that have 3 hands.