I know my local pets a home do sell small poultry drinkers but I don't believe they are mushroom ones. The other type will be ok, it just doesn't have a dome that sticks out like the mushroom one. You could still put some pebbles into it regardless of which one you get
I personally wouldn't put the coxoid treatment into their water unless you've seen signs that they are potentially being effected by coccidiosis. From my chicks being young, I add Verm-X Herbal onto their water every so often. It says to use from 2 months plus but I made the decision to use before, I just don't use as much. I only really do this for my Silkie chicks though since their immune systems aren't the best. My other birds don't get it from being young. I wouldn't use it in your case.
Yes pets at home will do puppy pads but they may be more expensive. They'll still do the same job just make sure not to buy scented ones.