As long as you are not a "US Person" (i.e., citizen, green card holder, resident) then the Form W-9 is not the right form. If you are being paid as an foreign (non-US) person, you should provide a Form W-8BEN. If you are being paid as a foreign entity, you should provide Form W-8BEN-E.
As long as the work was done outside the US and not connected with a US trade or business (or permanent establishment in the US), there should be no tax withheld or due. But you will need to provide the form, or they will be required to withhold taxes.