On KZ's, it more or less comes down to whether or not you have a permanent magnet alternator. Without the permanent magnet, you will need at least a small battery to energize the alternator.
The capacitor should be at least 50v, and probably anywhere from 4000 to 12000 micro-Farad will work. I use a 5000 micro-Farad (aka MFD or uF or uFD). The main purpose of the cap is to filter the alternator pulses so the regulator can work properly, and to smooth out the voltage pulses so the RMS of the voltage approaches the average of the voltage.
With a permanent magnet alternator, you can run batteryless if you are willing to make a few changes to the wiring. Mostly, you need to turn off everything to start it. That means lights, neutral indicator, gauge lights etc., but most importantly the headlight. A headlight acts like a dead short until the filament heats up and starts producing light. Then it's current consumption reduces to expected levels. That dead short will prevent the bike from starting. After the bike is started, you give it a small rev before switching the lights on. The small rev keeps the motor turning for the brief moment the headlight turns on.
I installed a relay to turn the lights off whenever the bike is turned off. The start button is used to trigger the relay to turn on after the bike is started.
Another possible change will be to the regulator wiring. If the reg/rec has a brown sense-line, that needs to be hardwired to the output of the reg/rec. This is because a capacitor does not have an inherent voltage level it wants to go to. A battery, naturally, wants to be around 13 or 14 volts. Any higher, and the battery will take current to pull the voltage down. A capacitor does not do this, so if the regulator is turned off, but the motor is still turning, as in right after the bike is switched off, the full output of the alternator might still be present and can pop the capacitor. Re-wiring the sense-line will prevent this.
Another issue is you may want the idle a few RPMs higher. If you are in the habit of letting the RPMs lug way down when leaving from a stoplight, you have a higher chance of a stall with the lights on. I bumped the idle up 100 or so to prevent this. Before that, I probably stalled it accidentally about once a year (usually when someone blows a redlight or pulls out of an alley unexpectedly and I have to slam on the brakes).
The key is to tune the bike so that it can start in one kick most of the time with a battery. If not, removing the battery will only make it more difficult to start.
The ignition has to be in perfect working order. The best ignition is probably the factory electronic system since it is the most efficient and uses no power when the crank is not turning. It only uses power when the crank is turning fast enough to switch it on. This means it does not drain the capacitor prematurely, as points may do, and as a Dyna S will surely do. A good working set of points with the dwell set using a dwell meter should work ok without a battery.
I should mention, I use two 55 watt halogen headlights (stock is a single 60 watt) with my batteryless bike. This means even at idle, there is plenty of power on a stock 3-phase charge system. It's only way below idle that power output drops quite a bit.