Are small clay capacitors pose any health hazards?
I think the real hazards are not from the substances these parts are made from contacting skin, but:

Swallowing.  These parts are not designed to the small part size quidelines for children that toys must adhere to, and I'm sure many are too small.

Pricking the skin.  Some parts are sharp and strong enough to puncture the skin if done with enough imagination.

Heavy metal ingestion.  I don't think that the metals in these parts pose much credible risk to skin exposure, but licking them or otherwise ingesting liquid, particularly acids (like most juices), that have come in contact with the parts may not be safe.  

Burns.  The parts themselves wouldn't burn anyone, but if you are going to solder them to assemble this jewelry, then there will be high temperatures involved.  Soldering iron burns are small and would generally pose no long-term danger, but they can hurt quite a bit for hours to a day.

Poking eyes.  Lots of small pointy things together with a number of small children doesn't sound like a good mix.



How serious these threats are depends on how young the children are, how many of them, and how well supervised.  Since you haven't told us any of that, you'll have to judge the severity of these risks yourself.