It sounds like you were issued a Municipal Court citation which charges you with having violated a city ordinance prohibiting Disorderly Conduct. If you plead "guilty or "no contest", or are found "guilty" as the result of a trial, a civil Forfeiture Judgment for money will be entered against you but you will not be sentenced to Jail. (Unlike a charge of Disorderly Conduct issued by the District Attorney's Office in the Criminal Division of the Milwaukee County Circuit Court, a Municipal ordinance violation citation does not involve a criminal charge.)
Disorderly conduct is generally defined as conduct that is violent, abusive, indecent, profane, boisterous, unreasonably loud , or which tends to cause or provoke a disturbance. Assuming your preparations to urinate had been limited to "looking for a place" to do so and had not advanced to the point where your "private parts" were exposed to potential public view when the officer intervened, your conduct does not strike me as meeting that definition.
Your description indicates that, despite your denials, the officer believes that you did urinate in public. It is not clear from your description what the Officer claims to have observed that led him or her to conclude that you had urinated in public.
If you proceed to trial in Municipal Court, the Prosecutor will need to have the officer testify regarding whatever observations he or she contends supported issuance of the "disorderly conduct" citation. You (or any lawyer you hire to represent you) would have an opportunity to challenge the officer's testimony through cross-exmination. You would also be able to testify concerning your recollections of what happened. It would then be up to the Municipal Court Judge to decide whether the preponderance of the credible evidences shows that you engaged in conduct that meets the definition of "disorderly conduct."
Whether proceeding to trial to defend yourself is "worth it" is a subjective determination which, ultimately, you have to decide for yourself. Likely, hiring an attorney will cost more than the $185 you would save if you proceeded to trial and won. On the other hand, if you simply plead "guilty" or "no contest" to the Disorderly Conduct ordinance violation charge, a record of that result might influence potential employers to avoid hiring you in the future. The City of Milwaukee Municipal Court has a website on which information about individual Municipal Court case proceedings can be accessed by the general public. Case information listed there includes the name of the Defendant and the nature of the subject citation.
I don't know what you mean by "MIC". If that is a reference to an adult criminal conviction of some kind that has not been expunged, the prospect of having a Municipal Disorderly Conduct forfeiture judgment concerning you listed in the Muni Court records might not not be as important a concern for future employment purposes as it might otherwise be.
You should consult with an attorney about your fact and circumstances. Most of them offer free consultations and will be able to spot any potential defenses at that time.
Responding to questions on AVVO does not establish an attorney-client relationship between the questioner and any attorney associated with Garrett Law Group, PLC. Responses should be considered and used for informational purposes only. Every case is unique in its facts, and all legal matters should be discussed with a licensed attorney prior to making any decisions or taking any actions.
If you feel your conduct did not constitute Disorderly Conduct, I would urge you to contest the ticket. However, though you believe your conduct was not disorderly, does not mean a judge or jury would agree with you. If there is a difference between your recollection of what took place and the police officer's recollection, the prosecutor (and most Judges, for that matter) will tend to believe the police officer's version of events. If your recollection and the police officer's recollection of the events are the same, then it is just a matter of whether the facts meet the legal definition of Disorderly Conduct. At the very least, you should get a copy of the police report to see if your recollection differs from the police officer's recollection of what occurred. If there is no difference, then you might want to contact an attorney to get his opinion of whether that conduct could/would be considered disorderly