I haven't converted a C15 so don't have anything specific to that model, but I have played with this sort of thing on both a Honda CB100 and a Triumph Blazer SS (a rebadged BSA and a descendent of the C15)
A lot of permanent magnet alternators on bike rely on the constant current characteristics of the alternator to limit the charging current. Where this is done they will often have two windings on the alternator. One will provide enough current to meet the normal current demands for ignition and to keep the battery topped up, and the other will provide enough current to meet the headlight and taillight load at night. This extra coil is usually switched in by an extra contact on the headlight switch.
With these permanent magnet alternators, the open circuit output voltage rises directly with speed. At low speeds the output will be too low to overcome the battery voltage, but as the speed rises it begins to charge. At higher speeds, the charging current cannot exceed the maximum that the alternator can provide, which is determined by the magnet flux and the number of turns. This provides a crude sort of regulation, eg one coil will provide an amp or so for daylight running, and the other will provide six or so for night running.
This sort of arrangement is fairly hard on batteries, since they are likely to get more charge than they need in some situations, leading to loss of water and harm to the battery. So some systems started to use various forms of simple regulator, usually shunt. Lucas in the early seventies started to use a Zener diode rated at about 120Watts in shunt. Around that time some larger bikes started to use proper excited field alternators like a car, with the equivalent type of regulator controlling the field. These are of course much better.
So what does this mean for conversion to 12 V? Well, at some low speed, the alternator is able to produce enough voltage to charge a 6 Volt battery. At some higher speed it will produce enough to charge a 12 Volt battery. The current it can deliver to the battery at higher revs will be about the same in both cases. So yes, you can just change the bulbs. It is preferable to add a regulator, especially if you decide to have both coils in circuit at the same time. The Lucas Zener would be fine if you can still get them.
In theory you could find that since it needs a higher speed to start charging, that you did not get enough charge when just going slow. In practice that does not seem to be a problem. However, if you are desperate for more lighting…my Triumph 250 was already 12 Volts, but the alternator developed a short from the winding to the frame. So I rewound it with a few less turns. This raises the speed at which it will start charging, but also raises the maximum current when it does. I was able to run a 120Watt spotlight, actually an aircraft landing light off a Cessna, on that bike, and it kept the battery topped up for long trips at night. With my CB100 converted to 12V I was able to run a 55Watt H4 halogen headlight, which was about adequate for the speeds that bike could do. Note that this was a better light than most of the superbikes had at that time, eg most early seventies superbikes had lights that were not adequate for more than about 50mph.
Note that you should not run the motor with the alternator and rectifier disconnected from the battery, as this is likely to lead to rectifier failure. One small Yamaha that I played with once was able to provide 85 Volts open circuit at maximum revs. The selenium rectifiers that the older bikes have will not cope with that sort of thing. Actually it is often worth replacing the selenium ones with a silicon rectifier, but that is another story.
John