What resistor (or indeed do I even need one)?
You talk about a single AA cell - about 1.5V, and a 3V adapter. So you need a resistor capable of dropping about 1.5V at 200ma - that would be 7.5 ohms. Power would be V*V/R or slightly over 0.25W. 

I would use an 0.5 or 1W resistor for the purpose, and expect it to get quite warm. Exact resistor value won't be too critical - if I had a 10 ohm resistor handy it'd just take a little longer to charge.