That tone sequence should probably be quite easy to decode from the WAV file into time and frequency. There are a number of free audio softwares that have FFT support allowing them to measure amplitude and frequence of the signal. And it isn't too hard to write a tiny program that does the same, while stepping the time.

But it was a very sorry sound, reminding me of very early game pads.

Exactly what does the customer want? Any way you can convince him to go with something a tad better? The sound in the mp3 player is good enough for a hobby project for for a school assignment. But I can't even see that the toys sold to 3-year-olds will sell with such a sound - the parents are not 3-year-olds and will select a different toy. Cheap microcontrollers can generate much, much, much better sound in software using a DAC or PWM output. It greatly helps to add a bit of echo, reverb or similar to get a bit more life in the sound.