Here is info from Help file for the TransferSpreadsheet action:
Has Field Names
Specifies whether the first row of the spreadsheet contains the names of the
fields. If you select Yes, Access uses the names in this row as field names
in the Access table when you import or link the spreadsheet data. If you
select No, Access treats the first row as a normal row of data. The default
is No.
When you export an Access table or select query to a spreadsheet, the field
names are inserted into the first row of the spreadsheet no matter what you
select in this argument.
Note the last sentence. It appears you cannot "turn off" the field names
using TransferSpreadsheet.
You'll need to either use Automation to write the data into the EXCEL
worksheet, or use Automation after the export to delete the first row that
has the field names. Neither of these can be done via a macro; you need to
use VBA code.