(For your application consider Vout of your converter = Vbat in my comments, below)
If you want to use them at "star" typical power levels, YES stars need a current regulator, or current limiter (such as a resistor or PTC thermistor) or a power limiter (if using a converter) to avoid thermal runaway.
One can run LEDs including stars, at voltages below the LEDs design Vf (applied Voltage forward) point, but with current so very low, the output is pitiful. For example, one white LED with nothing to limit the current might just begin to glow at 3.0V, cold. At 3.35V it might be at full rated output at room temp. At 3.5V warmed up, it would destroy itself in a few seconds. The current of a LED goes up exponentially (very steeply) around the specified Vf. The only thing limiting this is external resistance or other external current limiting-regulation.
I have a couple high Vf 5mm white LEDs running direct, one from a RCR2A LiIon, which I never charge above 3.85V, and one running direct from a tiny 3.6V (rated, ~3.9V fresh no-load) primary stack. These run around ~17mA max. The output is about half of an SMJLED. (From memory, my little LEDs are 2 year old, 10CD@30theta rated Nichias.) These setups rely on the higher Vf of the LED and the small but important internal resistance of the cell(s) and flashlight contacts. If the LEDs were to burn up, I would simply put in another 20 cent LED. (Way cheaper than a Mini-Mag lamp!) It hasn't happened yet.
Trying the no current limiting or regulation technique with power (1-5W) LEDs, either the output is as pitiful as my little LEDs above (when Vbat is well below normal specified Vf of the LED) or the LED burns up, going into thermal runaway (when one uses a Vbat at or near specified Vf, depending on starting temperature, heat sinking, and exact battery characteristics.) This failure is accelerated because as the LED temp rises, the Vf value of the LED drops, meaning for a given applied voltage, the current will be much greater. POOF!
SOMETHING outside the LED must limit the current (or Power, thus somewhat limiting current) or the LED will act like a fuse, after a short, bright, run.