You are making 2 opposing assumptions there, 1) there is nothing to bump into in outer space, the earth picks up 43 tons of new mass every day.

2. the earths orbit would decay, the earth is absolutely massive compared to the amount of mass gained, and also off gasses a significant amount of mass every day.

If orbits don’t decay, why do even high orbit satellites need to make elevation corrections?

If you put a small body into outer space it would absolutely be (slowly) effected by the miasma of particles out there.

And let’s not forget we don’t have a time table for reaching the sun, and we aren’t aiming for the middle of the sun to see results. And as you approach the sun you will bump into more and more particles as they too are being drawn around the sun.