USB power pack in wearable electronics: Is it safe?
Manufacturer is: 

TWINTECH INDUSTRY INC   
16420 MANNING WAY
CERRITOS, CA 90703 USA

UL File Number:  MH60879
Model: 2706UL RetroFIT 1500P

This unit was certified UL 2054 compliant

UL 2054 checks or tests the following:


Components
Casing and Enclosure
Electrolyte
External battery pack connectors
Printed wiring boards
Lithium Ion Systems Only
Temperature Measurements
Short-Circuit Test
Abnormal Charging Test
Abusive Overcharge Test
Forced-Discharge Test
Limited Power Source Test
Battery Pack Component Temperature Test
Battery Pack Surface Temperature Test
Crush Test
Impact Test
Shock Test
Vibration Test
2N Steady Force Test
Mold Stress Relief Test
Drop Impact Test
Projectile Test
Heating Test
Temperature Cycling Test






All Li-ion batteries and battery packs are governed by IEC 62133 and UN 38.3.

Some of the safeguards required for Battery Pack manufacturers:


Built-in PTC (positive temperature coefficient) protects against
current surges.
CID (circuit interrupt device) opens the circuit at a cell pressure
of 1,000kPa (145psi).
Safety vent releases gases on excessive pressure buildup at 3,000kPa
(450psi).
Separator inhibits ion-flow by melting process when exceeding a
certain temperature threshold.






LINK IEC 62133 Slide Presentation PDF

The sellers must provide a certification of compliance which will have statements like:


  The cell used is a UL recognized component according to UL1642. 
  The battery is certified according to IEC 62133 edition 2 and UN 38.3








The UN 38.3 test includes:

T1 – Altitude Simulation: Low pressure simulating unpressurized cargo hold at 15,000 meters.
T2 – Thermal Test: Temperature extremes by keeping batteries for 6h at -40°C and +75°C.
T3 – Vibration: Test simulates vibration during transportation at 7Hz to 200Hz for up to 3 hours.
T4 – Shock: Test simulates vibration during transportation at given G-forces relating to battery size.
T5 – External Short Circuit: With fusing, apply a short circuit at 50°C. Case cannot exceed +170°C.
T6 – Impact: >20mm cylindrical cell tested for impact; all &lt;20mm cell types tested for crushing.
T7 – Overcharge: Charge at twice the recommended current for 24 hours (secondary batteries only)
T8 – Forced Discharge: Same as T7, forced discharge with primary and secondary cells.



Reputable battery manufacturers do not supply Li-ion cells to uncertified battery assemblers. 

I assume your concerns are liability. You need to do your due diligence to ensure you are buying safe products from a reputable supplier.  To do otherwise would be negligent and significantly increase vulnerability. It's not cheap or easy for someone to sue you so if you do your job right you should be okay.  Buy only from a reputable manufacturer and document your due diligence.



You may be better off with NiCd

Depends on if the capacity required is available in small enough pack.
May improve efficiency, 1.2v/cell gives you more input options. 2.4/3.6/4.8


Safest most rugged
Can withstand charge abuse
Ultra-fast charging
Long shelf life 
Economical, lowest cost per cycle
Wide range of size and performance
1.2v/cell can get 4.8v pack
No transportation regulations


NiMH

Differences compared to NiCd

Cons


More delicate than NiCd 
Longer charge time
Less over charge tolerance
Less life cycles 300-500 vs. NiCd 1000
50% higher self discharge 30% vs 20%
Slightly higher internal resistance


Pros


Improved memory
Higher capacity 
Higher specific energy 60-120 vs 45-80
Less maintenance 
Available in AA and AAA cells