The light will likely be used to light from close range (i.e. lighting a dark room, the inside of a cabinet or the underside of a car), similar as an LED inspection lamp.  I see less used for pointing a bundle of light at faraway objects (i.e. to draw attention, see where you're going at higher speeds such as a bike light).

So we'll need a wide angle of light instead of a narrow beam.  That's why we'll use a COB-LED panel instead of a LED-STAR with a lens.  It leaves us the added benefit of lower cost.  COB-LED panels are very efficient.  The heat is spread over a large surface area, so a heat sink might not be needed (at least, that's the goal).

Option 1 :  "4W" LED-COB panel 50x20mm

AliExpress "Festoon light 12V" : €0.84/pce

As the housing shouldn't be longer than a 18650-cell, this panel fits nicely.  The cool-white LEDs are generally more efficient than the warm-white version.

LED voltage is "12V", so a boost-converter can be used to power it from a 4.2V Li-Ion battery.  The forward voltage is 10.1V at 300mA, 9.6V at 250mA.  The maximum current for this module without heat sink is 250mA.  The temperature rises by 45°C above ambient then.  This has been measured with a thermo-couple stuck to the backside.

It would be more correct to rate this LED-COB panel at 2.5W instead of 4W.

The 20Ω series resistor needs to be replaced by a 0Ω-resistor.  The resistor can't handle the power at a 300mA LED current (an 0805 resistor is not rated at 2W) and when powered by a LED-driver, this resistor isn't necessary anyway.

The two-sided tape has been removed because it impedes the heat flow.  Two-sided heat transfer tape exists, but it certainly isn't cheap.

Option 2 : "3W" LED-COB panel 60x8mm

AliExpress Sumbulbs Official Store : €1.03/pce

All LEDs seem to be in series in this panel.  The LED-voltage is about the same as a Li-Ion cell.  A boost and buck converters can't be used with a single panel.  We can put two panels in series and use a boost converter. 

The panels could be mounted on touching surfaces of the housing to get an even wider light angle.  The two mounting holes allow for easy mounting.

Some measurements:

• Forward voltage : 2.8V (at 650mA)
• Maximum current : 650mA without heat sinking the temperature settles around 56.5°C.  For that measurement, a thermocouple has been stuck to the back of the COB-panel.

without additional heat sinking, power consumption is only about 1.8W (maybe 2W if you allow for a higher temperature)

Once again, it would be correcter to advertise this panel as 2W instead of 4W.

Conclusion

Option 1 is preferred because of the lower current and higher forward voltage, this makes it easier to design an efficient and reusable (for other projects) LED driver. 

The only issue that needs to be solved is the mechanical attachment.