The code I posted would repeat a pattern every 60 hours, at a 10k sampling rate. I don't think you would notice that. 
As far as cost, I think something like a Pro Mini and piezo together might be competitive with a Zener/BJT source along with amplifier... even a proto board costs money.
Also, reading the original post again, why not simply try the suggestion you mentioned? Don't you think it would give you more concrete questions and experiences to post here?