Use a microwave motor to power LEDs
I've used one of those motors as a generator for one of my pet projects. They can provide a decent voltage at low RPMs, however these are AC synchronous machines which run at a speed much higher than 6RPM (determined by its physical construction, usually 1500RPM) so there is a gearbox in there with a high gearing ratio, which will require a lot of torque on the output shaft to generate anything useful... Since they're made out of plastic, you might damage them; so this needs to be tested. I wouldn't expect a high lifetime from one of these things even if it works.

Anyway, for your actual problem, it depends on how you are inputting your mechanical energy: can it be considered to be turning your generator at a constant speed? Then you could get away with using a resistor: since your LEDs are not a variable load, you can calculate a resistance value that will work. However, the mechanical energy required will be increased for the same load, since most of it will be lost in the heating of the resistor. 
If the source is variable, for example if it's hand-cranked, you need to use a voltage regulator to absorb the voltage variations and produce a solid constant voltage. 

Either way, the ripple of a single phase AC waveform once full-wave rectified is the peak voltage of the waveform (i.e. it drops right down to 0V every 20ms), so you'll need to add a capacitor to hold the voltage above the minimum input voltage of the voltage regulator if you're using one, or above whichever value will make your LEDs too dim if you are using a resistor. OR you consider 100Hz (twice mains frequency, because of the full bridge rectifier) is enough to take advantage of the retinal persistance, and you design the resistor for the average value, making sure the peak voltage will not damage your LEDs because of the increased current. This way, no need for a capacitor. 

Connecting a wall wart directly to the motor is similar to the voltage regulator approach, so there will be a speed under which your output will drop.

Bottom line: test it!