Basically you have the right idea. I suspect your wires are broken in the conduit if in fact conduit was run from house to shed. If not then you will need to dig a new trench and bury PVC and pull wires.
If the conduit is intact, try tying the new wires to the old and as you pull out the old, the new gets pulled in. It may or may not work. Get someone to help you. This is a job where 2 people can do the job easier than one. One pulls while the other feeds wire in to the conduit. Also buy a quart of wire pulling soap to slick up the new wire. It makes the wire easier to pull in.