I mostly see folks on here pimping the Mostenbockers lift-off graffiti remover available in spray bottles...but I find their other product that is lesser known has worked way better for me - especially on woodrail legs and rails - it used to be called Lift-Off Gel, but they seem to have removed the GEL word, and now just call it Paint and Varnish Remover. You can tell it's the right product by the spout opening.

It works good on stains too, hence the "varnish" I guess, which is once again very useful in woodrails.
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One of the reasons I tried the Mostenbockers I linked to was because it's got no dangerous chemicals...I use it inside - there is no dangerous vapors and it cleans up with water. Most paint strippers are very dangerous. Read the label of whatever you use!!

The Zinsser Amber Shellac is exactly what I use when I refinish wood rails and legs...but most of the time you can get away with the "laquer reflow" technique - obviously not this time for the OP - just adding that detail to show that most of the time re-finishing them isn't needed.