catch another process unhandled exception

You can try something like that to avoid the debugger question to appear, you won't get the exception but only the exit code:

class Program
{
    static void Main(string[] args)
    {
        try
        {
            ProcessStartInfo info = 
                 new ProcessStartInfo("ErroneusApp.exe");
            info.ErrorDialog = false;
            info.RedirectStandardError = true;
            info.RedirectStandardOutput = true;
            info.CreateNoWindow = true;
            info.UseShellExecute = false;

            System.Diagnostics.Process p = 
                System.Diagnostics.Process.Start(info);
            p.EnableRaisingEvents = true;
            p.Exited += p_Exited;
        }
        catch (Exception ex)
        {
            Console.WriteLine(ex.Message);
        }
        Console.ReadLine();
    }


    static void p_Exited(object sender, EventArgs e)
    {
        Process p = sender as Process;
        if (p != null)
        {
            Console.WriteLine("Exited with code:{0} ", p.ExitCode);
        }
        else
            Console.WriteLine("exited");
    }

}

In this question they provided another workaround for that, but changing some registry values.

If you are calling to a .Net executable assembly you can load it and (at your own risk :D ) call to the Main method of the Program class into a try_catch statement:

Assembly assembly = Assembly.LoadFrom("ErroneusApp.exe");
Type[] types= assembly.GetTypes();
foreach (Type t in types)
{
 MethodInfo method = t.GetMethod("Main",
     BindingFlags.Static | BindingFlags.NonPublic);
 if (method != null)
 {
    try
    {
        method.Invoke(null, null);
    }
    catch (Exception ex)
    {
        Console.WriteLine(ex.Message);
    }
    break;
 }
}

But be aware of the security risks you are introducing doing that.