"Waterproofing" or the act of properly shedding water off of the surface must be done from the exterior. There is absolutely nothing you can put over the exterior of your "shed" to make it waterproof, save from a membrane, drainage plane and another layer of siding realistically. Or a tarp but that is still very temporary.

A properly constructed shed will not leak.

If you shed has construction problems, are the leaks in the roof or side walls? Most leaks are in the roof area. If the roof leaks the best solution is to put a new roof on the shed.

If the side walls have holes allowing water to penetrate the building, cover the outside with properly installed exterior siding. You said the shed was 4X2. If that is the exact measurement, then three pieces of 4X8 exterior siding plus the corner trim should complete the job.

Don't forget to put a good seal around the door.

If the shed leaks badly, you may wish to consider replacing it with something like this from Lowes

https://www.lowes.com/pd/Arrow-Common-4-ft-x-7-ft-Interior-Dimensions-3-97-ft-x-6-45-ft-Yardaver-Galvanized-Steel-Storage-Shed/1002625520 

I had a second thought about what you said. If you problem is not leaks but condensation on the inside walls then you need to insulate the walls. Note: this would be a problem with a metal or plastic shed, There are several ways you could do that, I believe there is a hard surface foam that could be applied to the inside wall of the building. There are foam sheets that probably will work.. The purpose is to keep the warm air inside from contacting the outside. I don't believe wallpaper or tar paper would provide sufficient insulation. If tar paper was used it would bring its own problem as it sometimes oozes tar that could get on the contents of the shed.

Your scheme might work if there are frequent rain storms that form inside the shed,.

In case of rain storms outside the shed you may wish to apply a waterproofing strategy to the OUTSIDE of your shed.

If you are in a humid area, the fabric contents will grow mildew.