Please focus your evaluations only on the maneuver, not any aspect of stealth in space. I repeat: Stealth in space is not asked for, just the maneuver.
Let's take a more advanced world based on today. Due to increased efficiencies commercial and military spaceflight in the solar system became feasible enough to colonize the inner planets. Detection equipment such as cameras, radar and IR detectors remain mostly unchanged though, energy shields are a nono.
Now, my sleep deprived brain cooked up this possible 'stealth' missile deployment system and... now that I think of it needs concept evaluation:
Some kind of spacefighter flies with speed $\vec{v_0}$ and just disengages the missile during a maneuver (like in the middle of a hohman transfer to get into direcct weapon range) without engaging the missile's engines. For this one moment, the missile moves with $\vec{v_0}$, as does the spacefighter.
Subsequently, the spacefighter continiues the maneuver, not influencing the missile anymore. According to Newton's first law, the missile just goes on on its new orbit, reads passive data (radar or IR signature) and generates only minimal EM emission, only having the residual heat from when it was attached to the fighter - just enough to keep the electronics operational.
Once the missiles distance is short enough or some timer ran out, it uses maneuvering thrusters to turn to the needed new vector, starts up the engine and homes in. A particularly clever design variant might even just do a short corrective burn before 'hibernating' once again for a bit, trying to not being estimated as a big threat by the target as a hot burning item.
Now: Is this method for deploying your missiles in a tactical scale (single ship to single ship encounter) feasible or do I miss out some blatant flaw?!
I am not trying to disguise the ship dropping the missile or the missile at all. It is the basic maneuver that shall be evaluated: Does it give a tactical benefit to start a maneuver (like changing orbit), dropping the (mostly passive) missile as a 'dead drifting' object during this and having it launch later from its own orbit?
Since everybody is going over the BASICS of stealth in space: Yes, I read "There is no stealth in space.