It seems reasonable to put the unwanted population on a ship, then decommission the ship to get rid of the population. My experiments show this doesn't work. The population just magically appears at your nearest colonized planet. It could be a core world or a colony. It's possible to now have a colony with more than one population. Since the population of a colony doesn't normally increase, this could still be a good way to relocate races you don't want, but I don't know if that gives any type of bonus or any type of problem to the colony.
The creatures in space may help with your problem. I'm not completely sure about everything that can happen. Precursor sentinels can capture a colony ship, but they won't do anything with it. Some other race can now capture the colony ship and use it, so it will be their problem. I believe the same is true with pirates. Space monsters will destroy the ship and use the debris to make a new space monster. The former passenger will no longer exist.
I think constructors and transports may be the same as colony ships for precursor sentinels and pirates. They are definitely the same for space monsters, which will destroy any ship and make a new space monster from its debris.
Using the creatures in space will probably be more trouble than doing something else.
It is probably best to do what the others have suggested.