Dark matter density isn't typically radically different from the average density of visible matter in a galaxy. Reading data for Andromeda off Wikipedia its visible mass is about ##1.5\times 10^{12}## solar masses and its radius is about 76,000 ly, giving a density on the order of ##10^{-3}## Suns per cubic light year. Dark matter makes up about 85% of the universe, so you'd expect a density four or five times higher.
The solar system has a mass of about one solar mass and a radius (to the heliopause) of about 120AU or about ##10^{-3}## ly, for an average density of about 200,000,000 Suns per cubic light year, some two hundred billion times higher than the average density of visible matter in a galaxy.
Dark matter doesn't clump the way normal matter does, so you'd expect its density wouldn't vary anything like as much as normal matter. So (given the back of the envelope numbers above) I don't think there's very much dark matter in the solar system compared to the amount of normal matter. On that basis I would suspect that the impact of dark matter on solar system orbits would be on the low side of negligible.
You could add a uniform spherical mass density to the solar system and see what effect it has on orbital periods fairly easily. Then you could estimate how much mass density you need to have a detectable effect.