Are there some recommended approaches for running Bitcoin Core on a laptop with constrained storage capacity?
Yes as it has been said you can always use external drives to a save all your blockchain datas which will serve as you directory to be precise. It now depends on you find a suitable drive for it,you could use hard drives as you've asked.
How does this setup work,
I did some research for you and I found out a quote with a detailed explanation on how to go about it
It's a post made by HI-TEC99 on January 08 2017
[quote author= HI-TEC99
There is a way to to that if you create a shortcut to your Bitcoin-qt inside a folder you installed it to.
Right click your blackcoin qt Bitcoin-qt and select "create shortcut". Right click the shortcut and select properties. A popup should open containing a text box with the word target written to the left of it. Add the line of text below to the end of whatever is already written in it. Make sure there is a space between the text that was already in the text box and the text below.
-datadir=.
Press the apply button, then the OK button.
Double click the shortcut to start the blackcoin Bitcoin-qt wallet and it should store its largest files (the blockchain) and also its wallet.dat inside the folder containing the shortcut.
You can install the blackcoin qt Bitcoin-qt to a folder on a thumbdrive, use that shortcut technique, and when you double click the shortcut the blockchain and wallet.dat will get stored on your thumbdrive, not in appdata.
If you use that technique, and accidentally double click the qt instead of the shortcut a new wallet dat and blockchain will get created on your C drive inside appdata. Make sure you always start your wallet using the shortcut.
[/quote]
You can go through and follow the directions if there's seems to be no change in the aspect. It should help.