First problem.
Animal life is a parasite on plant life.
Cockroaches breathe oxygen released by photosynthesis, consume plant matter that was created by photosynthesis, eat animal matter that in turn was fed by plant matter created by photosynthesis.
The animal isn't capable of building its own nutrients, but rather relies on the complex organic molecules the plant has built. In an ecosystem that the animal did not evolve in, the organic molecules the plants use (for structure and energy etc) could very well be completely incompatible, leading to animals with in turn completely incompatible biologies.
If you consider this unlikely, the story of trees and coal should fix that. Trees (and hence wood) evolved many millions of years before organisms that could break down wood did. So huge piles of unrotting wood built up. These huge deposits of carbon are what most of our coal deposits are made out of.
Millions of years later, white-rot fungi finally figured out how to rot wood. And it stopped happening.
Our life forms co-evolved to eat each other.
The cockroach could arrive, eat things, and find nothing provides it with enough energy or nutrients to live. What more, everything could be poisonous or toxic to the cockroach.
Macroscopic life on Earth is relatively recent, and it exists in a specific kind of life-modified world. A different biology or ecology could easily result in an atmosphere poisonous to cockroaches and organic matter it cannot get energy or nutrients from.
Second problem,
Space is big
Firing stuff in random directions in space won't hit planets. Hitting a planet (besides Earth and the other planets of the Solar system) by firing in a random direction would be like firing a gun in a random direction, and hitting a specific target on the other side of the planet, 1000 times in a row.
Gravity won't "pull you into" planets, but would almost always just swing you into a new direction.
Next problem,
Stars are far apart
Launching something at a speed that it would reach the other side of the galaxy before, say, the Earth is swallowed by the sun, requires insane amounts of energy and technology.
Stopping such a projectile requires you to package insane amounts of technology and energy into the projectile, which is exponentially harder.
And then we reach:
The Galaxy has lots of stuff in it
Suppose you have perfect aim of star wisps. If you fired one per star, that is 100 billion stars.
We are already talking about a task that the entire human civilization couldn't pull off once, and you want to do it 100 billion times.
You need to rework your plan.
Start with a star-wisp based self-replicating mini civilization. This is already insanely hard, technology wise.
You launch a dozen or so of such wisps. They fly to nearby stars, quickly check for raw materials. If they see it, they stop. They then try to bootstrap their own industrial civilization.
After, say, about ten thousand years, 1 in 10 of them have the ability to launch star wisps in turn. Each launches a dozen wisps, at a rate of 1 every hundred years. (These are expensive to launch!)
So every ~10,000 years, you get 1.2 times as many wisps as you had the previous cycle, and start with 12.
To reach 100 billion wisps this takes 139 cycles, or just over a million years.
In practice, you are going to be more limited by the speed of light than replication rate; the galaxy is 100,000 light years from end to end, and your star wisps are probably moving slower than 0.001c (get going faster than that, then stationary atoms in the interstellar medium hit you like hard radiation. Not good). As with all exponential growth functions most of the growth happens in the last part, so after the local corner of the galaxy gets saturated you'll have a relativistic speed (even 0.001c is relativistic) wave of star wisps leapfrogging each other to colonize every system it can.
This star wisps armada can then build simpler things, like customized biological weapons, to disrupt any ecosystem it finds. However, more likely and usefully, it could instead seed dead worlds with life, or even try to redirect the ecosystems of worlds towards complex multi-cellular life and/or an oxygen atmosphere.
What more, 3d printing a human is a simple task compared to creating star-wisp producing civilization. So the armada could switch from spreading to invasion after it sets up a beachhead; the invading biologicals could be printed humans.
