Microsoft Excel – Stop Converting Copy-Pasted Values to Date

Select the empty fields (or the entire column), set them to a string format instead of the default value, and do a special paste (available on right-click) with "values only" to prevent a date format from being auto-applied.

(Moving Victor's comment to an answer, as per MSO, as OP and Victor haven't done so in a week)

I would use the Power Query Add-In for this. Power Query can read HTML files (local or web). It looks for tables so there will need to be some consistency in the HTML structure. Once the HTML table has been read, it will try to automatically detect dates - you can override this and convert columns manually.