I can remember many jobs we ended up remaking just do to the deburr problems on teflon and derin( was actually fater to make them then deburr them.
Deburring it on the machine is the best choice, hopefully it is still an option for you, Teflon and delrin were always a pain in the but for me and we rans thousands of parts out of them. we even used razor blades for cut off tools cause the parts were extreamly thin and they wanted no burr on the hole, but yet it had to be a sharp edge.
Depending on what the part looks like you might be better off making a fixture and squeezing the part in the then run a flat razor over the faces
we ran many repeat jobs and we had deburr fixtures just for this.
another way is to take a chunk of tool steel and grind a radius on it then chuck it in a drill press and run your part by hand around it.
if everything is smooth except the radius part it works really well.
another way is to get a scotch brite flapper, sandpaper flapper ( used on drill motor) even a brass wire brush will work and chuck it into the drill press or hand mill and run it by hand.
the whole key of cource depends on the corner break tolorance of your part and were it is.
scotch brite pads work but we have had customers say they dont like the finish from the pads