Before you swap over to a cap, you need to run some tests.
With everything turned off, measure the voltage across the positive and negative terminals of the battery. It will probably be around 6.2V or 6.3V for a healthy battery.
Now turn the bike on, start the engine, and let it idle until warm (at least a minute).
Repeat the measurement.
If the running voltage is the lower, then you don't want to remove the battery.
If the voltage is the same, it's possible that you can make it work, but still not advised.
Higher voltage is good. You'll probably be OK with the swap, but might need a few other tweaks to make it all work.
Assuming everything checks out, you'll want to select a capacitor rated at a voltage of at least twice the nominal voltage of your bike. Since you're running at 6V, you want a 12V capacitor (or more).
First, to understand why we need a capacitor, we need to look at how the power is generated for your electrical system. The alternator on your bike produces single phase AC power. Single phase means that the magnets on the rotor and the coils in the stator are aligned with one another such that you have a one-to-one relationship. The magnets embedded within the rotor are going to be roughly the same size as a winding on the stator. As the the first half of a magnet passes by a winding, it generates an increasing positive voltage. As the second half of the magnet passes by that same winding, the winding is exposed to the opposite pole of the magnet and a negative voltage is generated. This manifests as a sine wave of positive and negative voltage with an amplitude related to the number of windings per coil, the strength of the magnet, and the speed at which the magnet passes the coil. The frequency will be the same as your current engine RPMs. If you were to hook up the alternator to an oscilloscope, it would look something like this:
As you can see from the graphic, there are points in time where there is actually no power being generated by the alternator. This is when your capacitor kicks in to serve up the juice your bike needs. Without a capacitor to supply power until the next cycle of the alternator, your lights will likely dim and flash as power levels fluctuate. If the difference in power generation and consumption is great enough, it may even cause your ignition coils to malfunction and you might not even be able to get or keep the bike running.
So figure out what we need from a capacitor, it would be best to measure the current draw on your motorcycle so we can see how many Amps are pulled at idle. If that's not a possibility, we can also use the alternator Wattage rating to make some inferences. Lets assume 100W for your alternator (that's a pretty safe bet for a bike that size).
Usually, your bike would only be using about 80% of the rated alternator output (that's just a rule of thumb, not a hard and fast kind of rule). This is due to engineering tolerances and the like. No need to make an alternator too much more powerful than what the bike needs. This would be expensive and it would also be detrimental to the performance of the bike. This means we're using about 80W of power to run all the lights and the ignition system plus a little left over for charging the battery. Let's convert from Watts over to Amps by dividing by the voltage. In your case, we're looking at 13A. Since we're skipping the battery, we'll drop the Amp reading a bit more down to 11A.
So... our capacitor needs to supply the equivalent of 11A between each peak on your alternator sine wave. So how much time is between each peak? It depends on two things: The speed of your engine and the number of magnets on your rotor. Usually there will be the same number of magnets on the rotor as there is coils on the stator (if you're unable to determine the number of magnets). Let's call it 12 for argument's sake. The next thing we need is a worse case scenario on engine speed. Call it 400 RPM while you're kicking it over? So 12 x 400 is the number of cycles we'll see every minute. So 4800 cycles per minute is the same as 80 cycles per second. Dividing our power usage of 11A by 80 gives us a value of .1375A. But what unit is this? It turns out an Amp second is called a Coulomb.
I'm going back up a second here. Capacitors have two ratings. One is their maximum voltage and the other is Farads (usually rated at a MicroFarad, abbreviated as µF). A Farad is a Coulomb divided by the voltage differential within the capacitor. For all intents and purposes, a Farad and a Coulomb/Volt are the same thing (though not exactly, since the capacitor will experience a voltage drop as it discharges. This is academic though, and won't affect our real world application too much).
OK, back to the calculations. We need to be able to supply about .1375A at 6V to make up for the time where the alternator is not producing usable power. So our equation is looking like this: .1375A / 6V = F. This leads us to a value of .022916 Farads, or about 23,000µF. For safety's sake, double the voltage rating value of the capacitor to at least 12V.
