Presumably, if we have the ability to disaaemble entire planets, we more than have the capability to work around any orbital dynamic differences it brings.

Over long enough timescales (geologic, not human), you'd probably notice some changes in the paths of the inner planets, but I doubt you would see anything wildly different, and the outer planets would be mostly unaffected since they outmass Mercury significantly, and are much farther away from the Sun.

In order to keep a more stable Dyson Swarm though, free from most collision risk, those future engineers would probably aim to disaaemble every inner planet, stray asteroid, and the belt for materials. The gas giants would be last due to their mass, and because they're far away so their gravitational influence can be better mitigated with advanced technology.

This isn't something that would happen over a few thousand years or something like that, mind you. If we decide to work our way up to a Dyson Swarm, it could very easily be the project of a million years or more, starting with enourmous clouds of habitats and solar arrays slowly surrounding the planets and their Lagrange points as we need them, before they grow outward to independently orbit the Sun. Both because we won't have the population or industry to use all that excess energy and habitation space immediately, but also because it will take a long time to mine out entire planets out in the first place. It would be a very different world than the one we're used to now.