Wee

In a crowded city with no toilet in sight ( that is worst nightmare anybody can ever have ), I would seek for any corner which is dark and has nobody standing around , Immediately I will move to the corner and before anybody watches me or stops me or even looks at me I would ...............

It's a city, with lots of businesses around, right? A fast food place, coffee shop or restaurant would be the first place I'd consider using. If there's none anywhere to be seen, then go into a retail shop (clothing, shoes, bookstore) and explain your urgency. They will most likely understand and make an exception to allow you to use their employees only facility. Another option would be going into any office buiding with a entry lobby and ask their security guard if you can please use their restroom. Be polite, apologetic and very appreciative afterwards!

I would go into a cafe or a coffee shop and use theirs. In fact I have done this several times in the past. They are often cleaner than public ones anyway.