How to change the draggable icon of new theme
I suspect it's similar to a problem I had with draggable table rows in a zen subtheme: the icon was just a bit mis-placed. Using Firebug or similar tools you can see what's going on – on my site it looked like this:



Using firebug I could see the reason for this:



The icon was mis-placed. So I suppose you probably don't have to change the draggable icon itself, but you'll have to adjust the position of the icon. 

The css responsible for the position should look like this:

a.tabledrag-handle .handle {
background: url("../../misc/draggable.png") no-repeat scroll 6px 9px rgba(0, 0, 0, 0);
height: 13px;
margin: -0.4em 0.5em;
padding: 0.42em 0.5em;
width: 13px;
}


and you should find it in this system css file:
/modules/system/system.base.css

Instead of changing it in that system css file you should however override the settings in your theme's css file. You probably don't have to change much – just have to play around with the settings for margin and padding according to your theme… Hope this helps somehow?