If the sound you want is just a buzz, then the Arduino can drive a buzzer directly. If you eant music or recorded sounds played then the complexity jumps.
Acceleration sensors may not capture the complete movement. What part of the motion do you need to measure.
If WiFi is necessary then it can get bulky on a standard Arduino. An ESP8266 might be better.
Power consumption is an issue. How big of a battery can you fit and how long is it supposed to run?
A speaker has the advantage that i can control the volume. It is not required to play an audio file, just a single tone in a specified interval.
For the motion i dont need the complete motion. I only want to detect if the stick is in motion(walking) or not (lie on the ground). And i want to look if i can detect when the stick is put on the ground during the walk. This should show as an high peak!?
Size is not an issue.
Power consumption is not important. Its only a "prototype", i can even mount a powerbank for this purpose.