Is hashing an optional step to use with public key cryptography for blockchain
Questions like this cannot be answered without specifying the digital signature scheme you're using.

In general

In general, a digital signature scheme consists of 3 algorithms:


KeyGen() -> (PrivKey, PubKey): generates a private key and a corresponding public key.
Sign(PrivKey,Message) -> Signature: signs a message with a given private key.
Verify(PubKey,Message,Signature) -> Bool: verifies a signature against a public key and a message.


What the data types involved are depends on the specific scheme.

ECDSA

In ECDSA, the digital signature scheme used in Bitcoin, the private key is a number, the public key is a point on an elliptic curve, the message is a byte array, and the signature is a pair of two numbers.

ECDSA does require a hashing step. In fact, without the hashing step, it is completely broken.

However, nowhere is there any encryption involved. There is simply a signing algorithm, and a verifying algorithm.

RSA

The mistake you're making, calling signing "encrypting with the private key" is a very common one, because it is often how digital signature schemes are explained.

It is true for some specific signature schemes, but not all. Most notably it is true for RSA. The private and public keys are interchangeable there, so indeed, by swapping them, the encryption scheme turns into a signature scheme.