One solution that doesn't involve commands and bindings is to override the owning Window's OnKeyDown method and search a menu item that has a KeyGesture that matches the keyboard event.

Here is the code for the Window's OnKeyDown override:

protected override void OnKeyDown(KeyEventArgs e)
{
    base.OnKeyDown(e);

    // here I suppose the window's menu is named "MainMenu"
    MainMenu.RaiseMenuItemClickOnKeyGesture(e);
}

And here is the utility code that matches a menu item with the keyboard event:

    public static void RaiseMenuItemClickOnKeyGesture(this ItemsControl control, KeyEventArgs args) => RaiseMenuItemClickOnKeyGesture(control, args, true);
    public static void RaiseMenuItemClickOnKeyGesture(this ItemsControl control, KeyEventArgs args, bool throwOnError)
    {
        if (args == null)
            throw new ArgumentNullException(nameof(args));

        if (control == null)
            return;

        var kgc = new KeyGestureConverter();
        foreach (var item in control.Items.OfType<MenuItem>())
        {
            if (!string.IsNullOrWhiteSpace(item.InputGestureText))
            {
                KeyGesture gesture = null;
                if (throwOnError)
                {
                    gesture = kgc.ConvertFrom(item.InputGestureText) as KeyGesture;
                }
                else
                {
                    try
                    {
                        gesture = kgc.ConvertFrom(item.InputGestureText) as KeyGesture;
                    }
                    catch
                    {
                    }
                }

                if (gesture != null && gesture.Matches(null, args))
                {
                    item.RaiseEvent(new RoutedEventArgs(MenuItem.ClickEvent));
                    args.Handled = true;
                    return;
                }
            }

            RaiseMenuItemClickOnKeyGesture(item, args, throwOnError);
            if (args.Handled)
                return;
        }
    }