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Since neither of you want to press charges and it is a first offense the judge will likely send you both on your way with warnings.
Neither of you will get any jail time.
What is the likelihood that we will receive the misdemeanor, have you had cases like this?
It is unlikely you will even get a misdemeanor conviction, what is most likely is that the judge will isse you both a warning not to allow an argument to escalate this far in the future.
What would be helpful is to ackowledge that you both exercised poor judgment in allowing an argument to turn physical, you both have since resolved to handle disputes in a more rationale manner, and do not want to see the other person's unblemished record become tainted as a result of this unfortunate incident.