Assuming your governing statute, bylaws and policies don't provide any constraints or guidance, if the requirement is for a "signature" or that a document be "signed", I would request that each direct at least affix an electronic signature to the document, so that (1) you reduce the risk of any misunderstanding of exactly what is being signed; (2) you have better evidence of the director's approval (on the assumption they have better controls over their electronic signature than access to their email account); and (3) you'll then have evidence of approval (signatures) all in one document and you won't later have to go fishing for supporting emails.