<p>Is there any clever method out there to make my executeEveryDayMethod() execute once a day, without having to involve the Windows TaskScheduler?</p>

If the time when it is run is not relevant and can be reset each time the program starts you can just set a timer, which is the easiest thing to do. If that's not acceptable it starts getting more complex, like the solution presented
here
and which still doesn't solve the persistence problem, you need to tackle that separately if you truly wish to do what Scheduled Tasks would. I'd really consider again if it's worth going through all the trouble to replicate a perfectly good existing functionality.
Here's a
related question
(Example taken from there).
```
```
using System;
using System.Timers;

public class Timer1
{
    private static Timer aTimer = new System.Timers.Timer(24*60*60*1000);

    public static void Main()
    {
        aTimer.Elapsed += new ElapsedEventHandler(ExecuteEveryDayMethod);
        aTimer.Enabled = true;

        Console.WriteLine("Press the Enter key to exit the program.");
        Console.ReadLine();
    }

    // Specify what you want to happen when the Elapsed event is 
    // raised.
    private static void ExecuteEveryDayMethod(object source, ElapsedEventArgs e)
    {
        Console.WriteLine("The Elapsed event was raised at {0}", e.SignalTime);
    }
}
```
```