Yeah for sure! This method is a bit of a stretch but eventually, it'll be time-saving. Before doing anything, I hope you have all the songs in a playlist and have them downloaded locally to your PC / MAC.
So when you download a song on Spotify, it is saved in a location. If you want to see the location Spotify saves the songs, just go to your Settings tab and look for Offline Songs Storage. Then go to your Windows Search or Mac Finder and do %AppData%. I think it's the same for mac, but am not sure. Go back one step and select the folder Local. Then go to the folder Spotify -->Storage. You'll find a bunch of folders in it labeled something like ae, b1, 03, etc. Go to sort and sort by date modified. There will be a bunch of folders containing the same date, but when you open them, the file in them might be from a while back. Keep opening the folders until you come across a file where the date modified is your present date. Open that file with notepad and do Ctrl + F to search for one of the songs in your playlist that you want the name of. If that song isn't present, simply go back and open another folder and find another file with the present date. This might take a little bit, but once you find your song, all the songs you're looking for will be in it (along with a bunch of gibberish). I found my file in a folder called 07, but not sure if it's applicable here. Hopefully, there's an easier system in the future, but this is the only way I found right now.