Just so that you don't have to; I've got the pictures, insides of a 3.7 Volt DC air pump, for camping mattress.
On the left is a lithium battery; at
2000 mA-hrs. Switch is on right of photo. With a small control board with medium sized pwr transistor, that handles the charging over USB mini 5 volts. Sorry, that's likely not the exact term, for doing charging off of a wall wart.
Spec. is saying takes about 4 hours to charge.
Also, the fan-air pump motor should only be run for 6 minutes at a time, due to heating.