I would do it in the code-behind to prevent the markup from being sent at all.
If this is in an enumerable control (gridview, etc) then you can override the RowDatabound event to evaluate the value of the current gridviewrow and set alternateAccountNumberLabel.visible = false.
That will prevent .NET from even sending the HTML. If you prefer, you could also assign a CssClass that would toggle display:none; if you want the object to be available to manipulate via
js etc.