Just “shedding mass” won’t do it. Uncouple a payload from the mass of the ship at perihelion, and they will just float along together, side by side in their original orbit.

But, if that “mass” is “rocket fuel”, and you “shed” it by burning it behind you, you’ve got the right idea. As the other commenter said, the Oberth effect means the closer you are to the sun, the faster you are moving, and the greater the effect that burning will have.