^^ The link with the circuit designs is interesting. But I believe reliability is an issue as most don't address the LED's forward voltage limit and current draw. Typical of these high flux emitters, 3.6-4.0VDC is Vf. And 650-1000mA of current draw. No regulation in most of the offered circuits. And the complication level of the latter circuits is undesirable as cost and reliability become serious considerations IMO.
A better and simpler method is to combine both worlds so to speak. Implement a battery powered design with the generator as recharger. The spikes in its output are easily shunted by a rechargeable battery pack, offering flicker free light, plus more importantly, illumination while at a stand still. Just connect a full bridge rectifier to the dynamo to yield DCV and connect parallel to the battery pack. 4.5-6V is enough to drive a typical white LED. A limiting resistor in series with the LED is all that's needed for regulation. Or a switching power supply puck if you desire high efficiency. IMHO, it's not needed here, as the dynamo will extend the runtime of the batteries during a night ride.
It's just a down-sized version of what is every car's headlight system.

As for converting your existing incandescent dynamo light to batteries....
simple substitution of power source. BUT, you can do better just by replacing the set up with LED lighting. More light, less bulk. Unless you're wishing to preserve the look of the headlight, then search for a 3W white LED drop-in conversion bulb for your headlight. There are PR bayonet mount style bulbs for 3, 4.5 and 6V flashlights.