Extremely small electric shock device - could this work?
There is no such thing as 'standard size ring'. It would be pretty easy to fit anything into a ring like this: http://www.mindwhatyouwear.com/bigring.html

Otherwise, the circuit will have to be a boost converter which will slowly charge the capacitor, which will then be quickly discharged into the finger. How big of a capacity are we talking about?
Well, this forum thread talks about being shocked by capacitors:
http://www.diyaudio.com/forums/everything-else/27768-danger-capacitor-electric-shocks.html
Based on this, I would choose, say, 120 volt and 0.1uF.

The biggest components circuit will need to have:


Battery: MS412 is 4.8mm x 1.2mm: 





2x 200 volt mosfets: http://www.digikey.com/product-detail/en/EPC2012/917-1017-1-ND/2351743 is bare die, 1.6x0.8x0.8 mm
200 V capacitor: http://www.digikey.com/product-detail/en/C2012X7T2E104K125AA/445-7749-6-ND/2734459, 2x1.5mm
Inductor -- if we do not care about efficiency, we can make a custom  inductor by winding wire over the part of the ring (which will have to be made of ferrite)


Our battery is 1mah. At 1% efficiency (reasonable given that the parts are not the best), we will get 
1 milliampere * hour * 3 volt / (0.1 microfarad * (120 volts)**2) * 0.01 = 75 shocks