Help with reverse engineering a small PCB
I lack the tools/knowledge/skill to identify the other components,
  measure capacitor values and trace the overall circuit.


Now is a good time to learn!

Get a large sheet of paper, draw well spaced out symbols for all components and any test pads or board connections, and name each one (R1, C2 etc.). For any parts you don't recognize draw a generic box with the device's pins in their physical order. Obtain datasheets for any parts you can identify. Knowing what the device is supposed to do also helps, so gather any information you can such as user manuals, wiring diagrams and specification sheets. 

Then use a multimeter on continuity test to 'buzz out' all the connections, and draw the wires between components. To find where a trace goes you can follow it by eye (a strong light shone through the PCB may help) or just rake over the connections until you hear the meter 'buzz'.  

Next try to identify common connections such as ground and power, and redraw the circuit neatly with conventional layout (input on left, output on right, ground towards the bottom etc.). This could also be a good time to transfer the circuit to your favorite schematic capture program. Most designs are based on conventional circuit configurations and manufacturer's application notes. Identifying these patterns and laying out the circuit in the same way can help in understanding how it works, as well as providing a check that you have traced it correctly.  

Now you can do on-board testing of components such as diodes and transistors to determine their orientation and type. Your multimeter's 'diode test' function can identify diodes and bipolar transistors (which read like two diodes back-to-back). ICs can often be identified once you have determined what the pins are connected to and their probable functions. 

Capacitors may have to be unsoldered to read their exact values, but don't do this unless you really need to. Their likely values can often be guessed once you have figured out the rest of the circuit.

Most important thing is to treat the task like a crossword or jigsaw puzzle - enjoy yourself as you try to solve it! And as with any puzzle, if a part is too hard then do another bit and come back to it later.