is there such a thing as a wide belt sander attached to a flex shaft?
The basic issue is the required power.  Belt sanders are designed for aggressive removal of material.  The larger the surface area that is sanded, the more power it takes.  At 1/2&quot; to 1&quot; wide belts, the required power is low enough that small motors can handle the job.  Flexible shafts can also handle that (they have limited strength).
At 4&quot; wide belts, you need big motors, and a heavy duty structure to support everything.  You can find handheld 2&quot; belt sanders that are within the power range that can be battery powered.  You probably don't want to work with a belt the same size as your piece for the same reason you don't want to work with a smaller belt.
A reasonable compromise would be a 3&quot; handheld belt sander that you secure in a fixture that you make or in a clamping work table.  The motors for these are typically over 800 watts, which means they're normally plug-in, not battery-powered (although there are a few pricey professional-grade battery-powered ones).  There's a selection of inexpensive consumer models at the big retailers.
When not in use, the sander is the size of a handheld power tool, so it's easy to find a storage place.  The clamping work tables typically fold for storage, and are handy for a variety of uses (it is a general purpose work table, not a dedicated part of a sander).  You could make a tabletop fixture for the sander that would be relatively compact.  A 3&quot; sander and fixture would be considerably smaller and lighter than a 4&quot; tabletop sander.
I've seen videos of hobbyists who have made their own belt sander from wood and other available supplies that they power with a drill.  A drill motor will have enough power for very light duty sanding, but any significant load is likely to damage it.