Hiya 42knapp,
Just out of curiosity, how do you know the original finish is shellac? ...and a homeowner put a Minwax oil stain?...or oil finish over the "shellac"?
Shellac is a wonderful coating. Like all finishes, it has it's distinct advantages and disadvantages, but overall it is a very durable, hard finish - great for bookshelves, furniture, etc...Not so good tables and bar tops that could have standing water or even incidental exposure to spilled alcohol, though.
I don't understand the Minwax oil stain (or finish) over shellac though. That really wouldn't work all that well. If you decide to use shellac again, one of it's advantages is it can be applied over most existing finishes without damage...so, going over what's there wouldn't necessarily be a problem. I would not, however, put a poly over the shellac (existing or new). Toolseeker and Gymschu mentioned that in their posts and they were both dead-on.
Polys are decent enough coatings and provide plenty of protection in most residential exposures. Just as with shellac, they have their own unique advantages and disadvantages. One of the major disadvantages is they don't always play well with existing coatings - shellac and sanding sealers are 2 types of applications that shellacs sometimes have problems with. With shellac this issue is the naturally occurring wax that is present within the film and can wreak havoc in the poly's ability to both adhere and cure properly...with more common sanding sealers, it's the chemical soaps that are added to allow for sealers to sand easily that, again, interferes with a poly's ability to adhere and cure properly.
Personally, if I was doing this and knew the original finish to be shellac, I'd wipe the surface clean with mineral spirits to remove any waxes or un-cured oils that may have found their way to the surface of this woodwork over the years - then lightly sand with a fine paper. Use a tack cloth to remove any sanding dust. Unfortunately the areas that have alligatored are going to have to be sanded smooth - probably start with a medium grade paper (or sanding sponge) and followed with fine then ex fine...just enough to remove the texture and have a nice, slightly profiled surface for finishing. Again, remove all sanding dust with tack rags.
Then, I'd apply 1 or more apps of amber shellac by brush or spray (if you've never used shellac before, practice a little on spare boards to get the feel of the flow and drying of shellac - it's different than applying varnishes and polys). If the shellac is too high of a gloss, you can rub it out with oil and pumice (or rottenstone) and 400 - 600 wet-or-dry paper - or just rub dry with polishing cloth found at most independent paint stores.
Not everybody is gonna agree with me here but IMHO I think woodwork from the 1920's deserve a nicer looking finish than polys provide...
Best of luck to you and let us know what you decide - some before and after pics would be great.
P.S. to Gymschu and Toolseeker - I think the product you were describing is "Seal Coat" by Zinsser (not clear coat)...Seal Coat is a "de-waxed", 2# cut shellac and would be fine as a sealer for poly...