If soft shelled eggs are your only symptom, I don't think I'd jump to the conclusion that she has worms quite yet. Do you give your girls oyster shell? I mix it right in with their feed - others put it in a separate feeder. REALLY hardens the shells. I had some very soft shell problems until I started that.
As for safe/effective worming, and lice/mite prevention, here's advice from dawg53 - he's the guru!
Sevin dust will kill lice/mites. I use hay as bedding and when I change it out or put fresh hay inside the coop just as a replacement for soiled hay (not a complete changeout,) I lightly sprinkle sevin dust on the fresh hay. I lightly sprinkle some in the nests and pat it all down to let it settle.
As far as worming goes, there are many wormers to choose from. Worming depends on your environment where you live. If you live in a warm, wet area and the soil is moist most of the time, you might have to worm several times a year. If you live in cold, mountainous or desert area, you might only have to worm once a year or maybe even longer than that, it just depends.
Soil conditions are what you need to be concerned about, whether it's dry or moist. Due to my environment where I live, I worm once every 3 months, rotating wormers to prevent worm resistance to one particular wormer. I use Safeguard liquid goat wormer, Valbazen liquid cattle/sheep wormer and sometimes Zimectrin Gold equine wormer. Ivermectin due to its overuse in chickens as a miteacide has been been seeing large roundworm resistance in chickens. It will not kill cecal nor tapeworms. Ivermectin will not kill lice in chickens, only mites because they suck blood and chicken lice dont. Same for Eprinex. Wazine only gets rid of large roundworms. There are many types of woms that chickens can get. Therefore it's best to use a broad spectrum wormer to get rid of them.