Thanks @jremington. I took a look at those, and I found a lot of voltage sources. Seems like an LED would need a current source, right?
Option A
Load: 5mm white LED (COM-09850, < 20 mA, 3.2-3.4 V)
Current regulation: FemtoBuck (COM-13716) modified to provide 20 mA. Replace R2 with 4.7-Ohm surface-mounted resistor bought elsewhere. Requires 6 < Vin < 36. Any tips on sources for SMD resistors?
Battery: 9-volt alkaline battery
Evaluation: Efficient. Moderate cost. Requires more skill and available tools.
Option B
Load: 5mm white LED (COM-09850, < 20 mA, 3.2-3.4 V)
Current “regulation”: Current-limiting resistor only
Battery: 3 AA batteries, approximately 4.5 V
Evaluation: Inefficient, lots of wasted heat. Low initial cost. Relatively easy.
Option C
Load: 5mm white LED (COM-09850, < 20 mA, 3.2-3.4 V)
Current regulation: DIY circuit (e.g. http://electronics-diy.com/power-led-driver-circuit.php)
Battery: 2 AA batteries with boost converter (PRT-10255) modified to output 3.3 V and operate down to 0.3 V
Evaluation: Efficient? Moderate cost. Requires more skill and available tools.
If rechargeable batteries are used instead, a couple more options arise.
Option D
Load: 5mm white LED (COM-09850, < 20 mA, 3.2-3.4 V)
Current regulation: DIY circuit (e.g. http://electronics-diy.com/power-led-driver-circuit.php). The variable resistance would dissipate the excess voltage as heat, I think.
Battery: 24.5mm rechargeable 3.6V coin battery CR2450 (PRT-10319) with holder (PRT-08863).
Recharging: Adjustable LiPo charger with 24.5mm holder (PRT-14380). Can the load be wired to this board, or does the load need to be disconnected while charging?
Evaluation: Moderate efficiency. Moderate cost. Moderate skill.
Option E
Load: 5mm white LED (COM-09850, < 20 mA, 3.2-3.4 V)
Current regulation: FemtoBuck (COM-13716) modified to provide 20 mA. Replace R2 with 4.7-Ohm surface-mounted resistor bought elsewhere. Requires 6 < Vin < 36.
Battery: 2 x LiPo, 1aH, 3.7 V (PRT-13813)
Recharging: 2 x LiPo Charger/Booster, 5 V, 1A (PRT-14411)
Evaluation: Efficient? High cost. Requires more skill and available tools.
Option F
Load: 5mm white LED (COM-09850, < 20 mA, 3.2-3.4 V)
Current “regulation”: Current-limiting resistor only
Battery: 24.5mm rechargeable 3.6V coin battery CR2450 (PRT-10319) with holder (PRT-08863). Resistor to drop voltage from 3.6 to 3.3 V.
Recharging: Adjustable LiPo charger with 24.5mm holder (PRT-14380). Can the load be wired to this board, or does the load need to be disconnected while charging?
Evaluation: Efficient? Moderate cost. Relatively easy.
Conclusion
Looks like I need to invest in a proper soldering iron, stock up on some basic parts, and learn how to solder properly!