I need to change default icon for moving cells in UITableView.
This one:
You can also simply add your own custom reorder view above all others inside your cell.
All you have to do is ensure this custom view is always above others, which can be checked in [UITableViewDelegate tableView: willDisplayCell: forRowAtIndexPath: indexPath:].
In order to allow the standard reorder control interaction, your custom view must have its userInteractionEnabled set to NO.
Depending on how your cell looks like, you might need a more or less complex custom reorder view (to mimic the cell background for exemple).