It would be cool if there was an option in Bitcoin Core for disabling the system tray entirely.

changePassphraseAction(0),
    aboutQtAction(0),
    openRPCConsoleAction(0),
    openAction(0),
    showHelpMessageAction(0),
    trayIcon(0),
    trayIconMenu(0),
    notificator(0),
    rpcConsole(0),
    helpMessageDialog(0),
    prevBlocks(0),
    spinnerFrame(0),
    platformStyle(platformStyle)
{
    GUIUtil::restoreWindowGeometry("nWindow", QSize(850, 550), this);
    QString windowTitle = tr(PACKAGE_NAME) + " - ";
#ifdef ENABLE_WALLET
    
    enableWallet = !GetBoolArg("-disablewallet", false);
#else
    enableWallet = false;
#endif 
    if(enableWallet)
    {
        windowTitle += tr("Wallet");
    } else {
        windowTitle += tr("Node");
    }
    windowTitle += " " + networkStyle->getTitleAddText();
#ifndef Q_OS_MAC