Yeah. Been there, fought an enemy who enforced that combo. He was pretty hard to find, but the tracker/shapeshifter located him by smell

I'd pick Improved Invisibility over Stealth (though I really like Stealth and my mage employs both).
Every GM I played with so far allowed for a skill check to move silently while being invisible, but being absolutely silent and standing right in the middle of the room (even with concealment) might have been another call. Check with you GM first to avoid that can of worms.
That said, Stealth does a great trick to keep extracted targets silent while in your trunk. The aforementioned combination of concealment and chameleon coating also makes people pretty much invisible and there's no equivalent to chameleon coating /-4 to visual perception) for sound.
Food for thought: Can the spell silence a weapon whose projectiles move with less than speed of sound (and thus create not much sound themselves)?