Would "chuda" work here as well?
For 'thin', yes. I'm not exactly sure about the usage of that word in English, but "chuda" could have some pejorative associations (although that depends on the individual's feel). And it works already.
why not "szczupłym" i "szczupłą"?
You could use Instrumental if there was a noun phrase (szczupłym mężczyzną, szczupłą kobietą), but not if it's just an adjective. See here: https://www.duolingo.com/comment/16373167, especially Part 3.