Tube sound: Pre-amp vs. amp?

You do not say what your source is! Assuming it's CD, might it be your CD player adding the HF edge? Regardless, a tube preamp will reduce the HF edge, but it will not remove the transistors from your SS amp. Transistors have their own sound as well. In short, yes, a tube preamp will warm your system. Be sure to try your choices in your own system to be sure you get the sound you seek.

Depending on how high end your CD Player is you may try an inexpensive tube buffer stage in between you player and amplifier. Musical Fidelity makes one for $200.00 (much less used) that does this trick but may slow the tempo somewhat per recent reviews and feedback. I assume that there must be other models that are also low cost. Maybe someone at this sight knows of them. The con is that you will need another pair of interconnects to hook it up.

You do not have to replace both your amp and preamp in order to introduce the sound of tubes. However, if you add a tube preamp, make sure it's output impedance is low enough to drive the input of your solid state amp. You may also need to replace your interconnect with something more revealing if you add a tube preamp. There are many good tube preamps around, my personal favorites are the Audible Illusions Modulus and the Quicksilver line stage. That said, I do not use a tube preamp because my most of my gear has to reside in a piece of furniture and tubes require ventilation. I had a Berning TF-10 that sounded great but was slowly cooking itself until I switched to a solid state preamp (Classe) with Quicksilver Mono Tube amplifiers. This gives me a balance of solid state detail and control and tube warmth and bloom. I have also had to experiment with different cables in order to get the overall sound to gel properly. Before changing your current electronics you may want to experiment with some cables (try Harmonic Technology) and see if your can remove some of the edge you hear.