
Several years ago our local authority was considering leasing a cute little street-cleaner type machine that used superheated jets of water to get rid of chewing gum, graffiti and, yes, curbside weeds. I was much taken with the sales pitch that included a reference to weeds wilting instantly and a smell of gently boiled cabbage wafting down the street...so depending on the scale of the nettle bed you could try watering well with boiling water--no toxic residue, although I'd be unhappy about scalding worms.
Our nettles have taken over a bit this year. I have developed a bad allergy to them so can't pull them up any more because I break out in blisters. I'll let you know how we get on after I've dumped the kettle contents on them (I let the nettles flower first for our bees).