Being "detained" absolutely does have a specific meaning when it comes to a police encounter. An officer needs to have reasonable suspicion that you have committed a crime, are committing a crime, or are about to commit a crime in order to detain you. If you ask, the officer (eventually) either has to say "yes," in which case s/he must demonstrate that reasonable suspicion, or say "no," which means you are free to go.
No, you didn't say you'd just walk away -- fair enough, my bad. But I don't see what point there is in trying to procure more "psychological power". Asking those two questions is really all the "power" you need, legally speaking. I mean, do you really think stating instead of asking is going to give you the upper hand? If you say "Thank you officer, but I'm going to go now," you set yourself up to be stopped again, likely by a now even more irate cop.
I was in the very situation about a year back. Two cops stopped me when I was walking home from work in the evening. I was doing nothing suspicious -- I live in a very small town and I had just moved there, so I figure they had probably seen a new face around town and wanted to know who I was. They told me they had gotten a phone call about a "suspicious person" who apparently had my first name and the last name "Smith" walking around town. I'm guessing they asked the clerk at the convenience store next to my office and got my first name, and then just cooked up a last name to fabricate the story -- I mean, Smith? Come on.
Still, though, I had no way of knowing if there was more to it than that. By asking if I was being detained, it forced them to essentially admit that there was no probable cause or reasonable suspicion. If they hadn't fabricated the whole thing and actually *had* received a tip, they might have had a reason to detain me; but then they would have had to defend it in court, which obviously they chose not to, which makes me think they had nothing to begin with. I don't know for sure, but that's the best I can make of it. Either way, it's much safer to just ask if you are being detained and get an answer from the horse's mouth.
But if you want to try your way, please do, and please upload the results.