I'm a firm believer in reusing jars used in finishing as much as possible. Especially very small jars that are handy for the small amounts of mixed finish that a single project often calls for, I will often go to the trouble of cleaning and reusing them. However, if the jars are common it often isn't worth the effort to clean them.
While it sounds like it would be better for you to just get more jars since you asked about how you might reuse them efficiently here's an option. Rather than using copious amounts of denatured alcohol (which will certainly work but might be considered a waste of the solvent) you can clean using a basic or alkaline water solution.
Shellac is soluble at high pH, hence one of the common old methods of removing it relied on ammonia.
If you make up a strong solution of washing soda that should be sufficient to clean the jars of shellac residue, and it will work even better if it's warm or hot. Best to wear gloves when doing any scrubbing that may be needed1.
A caustic soda (lye) solution will most definitely work too although lye is more hazardous to use and handle, and great care should be exercised if you go this route2. And of course the aforementioned ammonia will work if you can get that cheaply where you are. Use appropriate cautions with ammonia3.
shellac... now past [its] expiry date
Just to touch on this. There are rules of thumb about when shellac should no longer be used but be guided by what you have there. Proscriptive rules about how long shellac lasts once made up into liquid form are not to be relied upon because they take no account of the variability of shellac, a natural product (that may be further processed), and varied storage conditions.
Despite how long it's supposed to last once made into a liquid different users report wildly different shelf lives for their shellacs. Shelf life differences vary based on their local conditions, the type (colour) of the shellac in question as well as the age of the flakes.
With "past its expiry date" shellac test it and see rather that toss it based on an arbitrary date. If it dries fast enough, doesn't remain soft or sticky then it's still good.
1 Because the solution will tend to de-fat your skin. If you've ever washed your hands too many times with soap you'll know what this feels like and will want to avoid a recurrence.
2 Gloves and eye protection should be considered mandatory when using lye. Read up on the dangers if not familiar with it! And something not always mentioned, be sure to use a container that can take heat — lye going into solution is an exothermic reaction and at the extreme can boil the water.
3 The fumes aren't pleasant to inhale and can sting the eyes so it may be best to work outdoors. Just to note there are still very strong solutions of ammonia available in some markets (stronger than common "household ammonia" dilution) but my advice would to be steer well clear of them for this purpose unless you know what you're doing.