There's already been a discussion on something similiar that i think you might find useful.
Does password protecting an archived file actually encrypt it?
Also, from what i read from there WinRar uses a 64 bit key( WinRAR uses 262144 rounds of SHA-1 with a 64-bit salt), which is pretty strong.
I'm not 100% sure on the following, so anyone correct me if i'm wrong.
From what i understand when you encrypt a compressed archive or zip file, 7zip or winrar, the encrypted files doesn't let you read a key if there is one, as it is, encrypted. That would be the same as trying to decrypt an encryption without the key, so i'm pretty sure you can't get the key from the zipped file.
Also i'm not sure if it even stores the key. RSA encryption is one of the strongest encryptions(if you go for 2048 + bit encryptions), and some zip archives use the same AES encryption. The key isn't stored in the encryption, but the algorithm used to decrypt the file. The key is provided by the one who password protected/encrypted the file in the first place, and if the decryption key matches the encryption key, the algorithm will unravel the decryption, thus making it readable.
Does this answer your question?
Edit: As for just extracting the string with the encrypted decryption key, no. That wouldn't work as the key would be encrypted and useless, and you'd have to decrypt it to be able to read what the decryption key actually is, thus you're back at square 1.
For example, if i write: "pancakes", as "H01LG32H4Gg6H", you wouldn't be able to extract that encrypted string and convert it, as you don't know the algorithm i used to decrypt the word.