Crypto-shredding a file by erasing the IV instead of erasing the Key
No, just erasing the AES-CTR IV is not enough to reliably render the file undecryptable.

To see why, consider what happens if the AES key is later compromised, and the attacker also happens to know at least one AES block (i.e. 16 bytes) of the "shredded" file's plaintext content.  They can then XOR this known plaintext with the corresponding part of the ciphertext to obtain a block of the AES-CTR keystream.

Running this block through the AES block decryption function, using the compromised key, will then reveal the input block (i.e. nonce and counter) used to generate this block of keystream.  Incrementing and/or decrementing the counter will then let the attacker decrypt all other blocks of the file.

Ps. Similar attacks are also possible on all the other classical block cipher modes of operation (CBC, CFB, OFB, CTR).  I'll leave figuring out the exact steps needed as an exercise.  (The diagrams on the Wikipedia page I linked to should be helpful.)  With CBC and CFB modes, the first block of the file cannot be decrypted without knowing the IV, but on the other hand, those modes allow all the rest of the file to be decrypted even without knowing any of the plaintext in advance.

Modern AE modes aren't generally any more resistant to such attacks, either, especially as most of them simply combine one of the classical modes (usually CTR) with some message authentication scheme, and can thus be attacker just like the underlying classical mode.

The take-home message from all this is that the IV is not a secret, and hiding it is not sufficient to protect the message from decryption by anyone who has the key.  More generally, modern encryption schemes are generally designed with the assumption that the only secret parameter of the system is the key, and with the goal of remaining unbreakable as long as the attacker does not know they key.  The flip side of the coin is that, if the attacker does know the key, these schemes generally offer no security guarantees whatsoever.