Given the musty smell I would say that it is almost impossible to appraise this from afar. If their is mold/mildew on the box I wouldn't pay anything for it, because the box would be useless and the contents likely as well. In that instance I would remove the shrinkwrap to check the contents, but many others would not, because the tattered icky plastic is somehow considered to be of value, when its actual value (if original shrink) is guaranteeing at a distance that the contents are untouched and complete. But if there are potential mildew issues, that guarantee is moot; hence why I would remove the plastic and check the contents. Again, this is predicated on there being mildew on the box exterior.

i would leave shrink where it stays... value depends significanlty on its presence... the point that Stratochamp outlined has to be worked out if you dont want to have trouble in a sale: those gray/greenish halos on the back of the box are mold or not?
The value may swing a lot depending on the reply of this question.
ciaooo

I would carefully remove as much of the dust from the SW that you can.  If there are any holes in the SW, work around them, blocking off the hole with your finger or some other item that won't stick to the SW or box.  You can then carefully wipe off the remaining dust with a soft cotton or microfiber cloth and a mild cleaner that doesn't leave any residue, like a glass cleaner.  I've successfully done this many times without destroying the SW.  It looks like it could easily be done with this box, as I see only 3 or 4 spots where there might be holes in the SW.

The areas where the dust has found its way inside the SW will be the hardest to clean.  In these areas, a vacuum can be used, but it has to be set to low suction, preferably using a micro attachment.  To facilitate, a fine paint brush can be used to loosen up the dust just prior to vacuuming.  What you don't want to do is spread the dust around inside the SW.  It's much harden to get out then.  Judging from the pictures, it doesn't look like a lot of dust in underneath the SW though.

If you decide to clean it up, please post picture afterwards.  If there isn't any mold/mildew on the box, there is a better chance that there isn't any inside or any rust as well.  You said it was in an attic, so it's possible that the humidity was low, and this set has mostly been exposed to dust and heat.

You really can't hurt it if you follow those steps and don't rush.  The plastic was meant to be handled.  Even if you somehow get some of the glass cleaner on the box, it's unlikely it will do any damage as it will dry rather quickly.

The key is to remove as much of the dust first before wiping down the plastic with a damp cloth.  Don't spray the cleaner on the plastic directly.

Try a small area on the back first to boost your confidence.