Does the oath of ẓihār atone like a regular oath?

The expiation for ẓihār (a pre-Islamic form of divorce) differs from the expiation for an oath. The expiation for ẓihār is sequential: first, freeing a believing slave before intimate contact; if one cannot find a slave, then fasting for two consecutive months before intimate contact; if one cannot do that, then feeding sixty needy persons, as Allah Almighty says: "And those who declare ẓihār from their wives and then wish to go back on what they said - then [theirs is] the freeing of a slave before they touch one another. That is what you are admonished thereby; and Allah is Acquainted with what you do. And he who does not find [a slave] - then a fast for two consecutive months before they touch one another; and he who is unable to do so - then the feeding of sixty needy persons. That is for you to believe in Allah and His Messenger. And those are the limits of Allah, and for the disbelievers is a painful punishment."

As for the expiation for an oath, one has a choice between: feeding ten needy persons from the average of what one feeds one's own family, or clothing them, or freeing a believing slave. If one cannot find any of these, then one must fast for three consecutive days, as Allah Almighty says: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths. So its expiation is the feeding of ten needy people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever does not find [or afford it] - then a fast of three days. That is the expiation for your oaths when you have sworn. And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful."