I'm so sorry to hear of your loss.
You state you got your Silkies about 2 months ago, and to date they haven't laid?...how old are they? Were they laying before? Transition from one place to another can definitely interrupt the laying cycle especially since it would have been in late winter, a normal time of decrease.
Are any of the other birds looking under the weather? A decrease or lack of laying can also signal flock illness. Are there any subtle signs of teary eyes, nasal moisture, a mild "nicking?" That can be a sign of a Infectious Bronchitis or Newcastle disease, especially since you've lost one bird who had lethargic symptoms then death (another potential sign of IB....some birds are more susceptible.)
Hopefully it was the vent gleet...although that in itself doesn't generally kill a bird unless it was really bad and had become systemic.
A high infestation of lice can also cause poor/no egg production. It is safe to use DE on the chicks. I can't find my link, but it is my understanding It is safe to use Permethrin poultry dust on the chicks too.
Wazine (Piperazine) is not rated for young chicks (under 4 weeks)...so your plan to make sure the water is where they can't get to it is a good idea. The poo however shouldn't hurt them as they won't be eating it outright...whatever tidbits they pick up should be fine, and the worms are killed/paralyzed. You should be aware that Wazine only works for roundworms...it is not a broad spectrum wormer.
http://www.drugs.com/vet/wazine-17.html
You might consider using Rooster Booster Mulit Wormer. After my flock came down with Infectious Bronchitis, I used Rooster Booster Multi Wormer (for all chickens, not just roosters...simply the name of the company) to knock out opportunistic worms and to boost their overall health. Rooster Booster is fine for young chicks per the company's website.
http://roosterboosterproducts.com/ They only have to be able to eat the pellet, but if they can't, as it is a larger hard pellet, mom may break it up for them, or they simply won't get the wormer, so there is no fear either way.
Rooster Booster Multi Wormer is Hygromycin B (the wormer) and Bacitracin (a mild antibiotic) plus vitamins, minerals and probiotics. It is placed in the feed 1 scoop per 1 pound of feed and it targets 3 of the major worms (round worms, capillary worms, cecal worms) plus adds in a mild antibiotic. While intended for continuous feed, many use it for 2 or 3 weeks seasonally (and herbals inbetween). I used it for 3 weeks after my flock had IB. It really helped to perk them up and quell the final lingering coughs and any opportunistic bacterial ifnections (after the viral IB). It might be a good idea as you don't know what you may be dealing with.
I purchase it from A Better Chicken as I find it there at a better price than at the feedstore:
http://www.abetterchicken.com/product/50101
Hopefully your loss is something limited to just the one bird. Good luck with treating your flock.
Lady of McCamley