Hello there. Thank you for considering Wowza for your streaming needs and welcome to the support forum.
As you pointed out, every client (browser/player/device) has its own way of handling a 404. And there is nothing built into Wowza to modify the handling.
With some custom work however, you could override the play command to catch the StreamNotFound. This will allow you to display a custom message, or play a default file.
Something this might work, I didn't test it though:
If you need further assistance setting this up, I would advise to post a request to the find a consultant forum
public void play(IClient client, RequestFunction function, AMFDataList params)
ModuleCore.play(client, function, params);
params.set(PARAM1, new AMFDataItem("404"));
params.set(PARAM2, new AMFDataItem(0));
params.set(PARAM3, new AMFDataItem(-1));
// params.set(PARAM4, new AMFDataItem(true));
this.invokePrevious(client, function, params);