Forget anything excel will do itself if you want a totally clean export create a macro and write a file yourself below is about as simply as i can get the code and the only tags you will have is table, table row and table cell plus closure tags you can use completly as is you just need to make sure there is a c:\temp folder otherwise just change path and filename to suit.
Sub export_To_HTML()
Dim HTML_Ouput
HTML_Output = HTML_Output & "<Table>" & vbCrLf
Open "C:\temp\MyFile.HTML" For Output As #1 'Simply name the file what you want
For HTML_Rows = 1 To ActiveCell.SpecialCells(xlLastCell).Row
HTML_Output = HTML_Output & "<TR>"
For HTML_Cols = 1 To ActiveCell.SpecialCells(xlLastCell).Column
HTML_Output = HTML_Output & "<td>" & Cells(HTML_Rows, HTML_Cols) & "</TD>"
Next
HTML_Output = HTML_Output & "</TR>" & vbCrLf
Next
HTML_Output = HTML_Output & "</Table>"
Print #1, HTML_Output
Close #1
End Sub