You would need to insert the text Table A-1 in the appendix and then assign a bookmark to it, such as TableA1 and format the font so that it is hidden.
When you insert the cross reference to the text of the bookmark, it will also appear with the font attribute set to hidden, but if you remove that attribute, it will not be reinstated if the fields in the document are updated and the cross reference will function in the same way as any other cross reference.
With the display of hidden text not in effect, you will not see the Table A-1 in the appendix.