Ministers have to sign thousands of documents, and even deputy ministers do. The Clerk of the Privy Council has to sign probably hundreds of thousands. And normally the act of using that signature machine is a very carefully managed and guarded act, so that only documents that that person feels should be signed are signed.
As I understand it—and I can be corrected on this—in the law it's irrelevant whether the signature is made by a machine or by hand. As long as it's done under the authority of the person whose signature it purports to be, it is construed as the personal signature of that individual.