I'm probably stating the obvious here, but whatever your strategy for decrypting is you still must verify the ciphertext integrity, which unfortunately for you is calculated on the whole ciphertext. You may win some time by not reading the stuff before the block you're interested, but you will have to read the whole stuff anyway if you want to be safe.
I'm no expert of course so I don't even know if there's an AEAD that can bring you integrity on parts of the input; at least I know that minilock (https://github.com/kaepora/miniLock/blob/master/README.md#-m...) builds some kind of counter mode where each chunk is properly encrypted and has everything needed to check its integrity.
The most widespread way of using Salsa/ChaCha is in the "Chapoly" construction, which combines ChaCha20 with DJB's Poly1305 polynomial MAC; this is an authenticated construction. Pretty much every mainstream application of Salsa20 is in fact a Salsa/Poly1305 construction.
You can also just combine Salsa and HMAC.
It's true that you need to authenticate your data, but this is true for any cipher that you use.
It's a bad idea to implement your own cipher code, no matter what you're doing. If you're looking to include Salsa/ChaCha in an application, use Nacl, which refuses to give you unauthenticated ciphertext.
I'm no expert of course so I don't even know if there's an AEAD that can bring you integrity on parts of the input; at least I know that minilock (https://github.com/kaepora/miniLock/blob/master/README.md#-m...) builds some kind of counter mode where each chunk is properly encrypted and has everything needed to check its integrity.