In a couple places, the Gemorrah looks for a possibility of someone who knows Shabbos but doesn't know any of the Issurim or Punishments and answers "Techumim" according to Rabbi Akiva.
Could the Gemorrah have also given the answer of Mechamer (using an animal) for which I don't think there is a punishment of Kares or Sekillah
Good point! The Rishonim ask your question, and answer a clear and simple answer: Mechamer means walking after your animal while it is doing Melachah . The RASHBA explains that if a person does not know that a human cannot perform Melachos on Shabbos, the Gemara considered it ridiculous to suggest that he knows that animals cannot do work on Shabbos.
(We discussed other points, related to the Gemara's question, in our Insights)
Be well, Mordecai