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You will need to create a movieclip symbol for customized cursor design then you will have to type in few lines of code asking flash to hide the existing cursor and show the new cursor developed by you.

Create a Movieclip symbol 

Steps to Follow :

1. Press (CTRL+F8) to create a new symbol. Select "Create New Symbol" window will appear

2. Name your symbol cursorNew_mc.

3. Click on movieclip behavior and then press OK. Now you would have entered your movieclip symbol.

4.  Draw anything you like to replace the existing cursor.

Now come back to "Scene 1" which is your main movie. To get back to "Scene 1", click on the "Scene 1" text on top of your timeline window as shown in the figure below.

In "Scene 1" of your main movie

1. Drag your cursorNew_mc movieclip symbol from library onto your stage. If library window is not open, Press (CTRL+L).

2. Name this Symbol "cursornew" in the instance text box of your property window.

3. Select 1st frame of your "Layer1". Go to actionscript panel (press F9).

4. With Frame1 of your layer 1 still being selected, type below mentioned script in your action panel.

    Mouse.hide();

    startDrag(cursornew, true);

5. Press CTRL+ENTER, to result programe.

Source : www.entheosweb.com