The original finish is 99.9% likely to be a spray lacquer or polyurethane so an alcohol shouldn't have any effect on it. That tip works with French polish because alcohol is the solvent for shellac, which is what French polish is (French polishing referring to the method rather than the finish itself).
What is the procedure for stripping? Is it just sanding down to bare wood?
You can remove finishes by sanding but it's not a good way to do it. I meant using a chemical stripper. It's a messy job but it removes the finish with minimal risk of damaging the tabletop.
Are you woodworker? If you have a card scraper you can scrape finishes from wood and it's actually a great method for large flat areas where speed is a requirement, but like sanding it takes some wood from the surface so will remove any built up 'patina' from light exposure (only using quotes here because of the age of the piece). But with something of this vintage that'll soon come back.
As for finishing, do I just apply the wax I have onto the bare wood, or do I need to do something else first?
You could apply wax directly to the wood but it wouldn't provide any real protection, wax is both too soft and applied too thinly to protect even from water.
You can refinish it in any way you like of course, for my money oil-based polyurethane is hard to beat. You'll be able to achieve good results as a first timer using an inexpensive product, with little or no specialised equipment (don't even need to buy a brush if you don't want to!) and the resulting finish both looks good and has excellent durability.
The method I'd advise is diluting it to turn it into wiping varnish which you then literally wipe on the wood. You should be able to read the sample pages from one of Bob Flexner's books on Google Books, here
. Pages 34 and 35 pretty much tell you all you need to know to get started.
And there's little else you need to know to complete the job, at its simplest with wiping varnish you just continue to wipe on coats and wipe away excess until you're satisfied with how the thing looks after the initial drying period, which given the time of year will probably be overnight or a bit longer.
For a working tabletop I'd go with at least four coats, do more if you want better durability.