With one exception, I’ve always p/ex’d my outgoing car against the new one as I like the convenience of getting out of my old car and straight into the new one.
I personally wouldn’t want the potential hassle of the time wasters and tyre kickers that you might get with a private sale. And as you’ve said, do non genuine buyers just have an ulterior motive for finding out where you live? Also, if you don’t get much interest in your for sale ad, you may find you have to drop the price, so could end up not getting much more than you would if trading in.
Good examples of in-demand cars were holding up value-wise exceptionally well three months ago when I traded my car in so you may be pleasantly surprised by what a dealer would offer for your car. You may find you have the upper hand. Always do your research though so the dealer doesn’t give you a load of BS.