>We calculate launch angle/trajectory using sophisticated algorithms to determine their destination.

It's a cruise missile, so no you cannot tell, unless it's a very simple missile with very very simple programming.

The reason you literally cannot tell, is that it's ambiguous until a later point in its journey. Before that a cruise missile aimed at another target could also have taken the same path up to that point.

And as far as can we tell whether a Kh-55 has a nuclear warhead, or a concrete warhead? No we cannot. They look the same from the outside. They might have ever so slightly different slight characteristics, but per-missile flight characteristics are going to vary more than whether they have a warhead, so again no one knows except those who launched it (well I hope they know).