Yes. It is possible. There are a couple different methods.
The first method, is to go into the iTunes settings & enable the iPod to be used as an external hard drive. So when you plug the iPod in, it shows up on the desktop as an external drive & you can then open it up & go through the files to find the songs you want.
Second method, is by using third party software. Instead of me linking you to a bunch of programs, I will let you decide which is best, based on your computer & operating system. What you want to (Google) search for is, iPod recovery software, or iPod to computer transfer. There are a bunch of programs out there that are easy to use & a lot of them are free. Although, you may be able to use just the trial of a program, as the trails usually limit you on how many songs you can transfer. Seeing as all you need is just the 4 songs. You could get away with using just a trial.
The programs are simple & pretty much all work the same way. With the iPod plugged in, open the program – which will look like a simplified version of iTunes, which lists all the items on the iPod. Then you just check off the songs/photos/videos/etc, that you want to transfer to the computer’s hard drive & click a button. Done.
I am on a Mac & have used Senuti to recover songs in the past & it worked very well.