Would a OTP No-Key Protocol work?
Would this still be a valid and comparably secure protocol as Shamir's No-Key protocol?


No, it would not be secure at all.

In this revised protocol, Alice sends a message $M$ to Bob, to do that, she picks a random string $A$, and sends:

$$A \oplus M$$

Bob receives this, picks a random string $B$, and sends:

$$B \oplus (A \oplus M) = A \oplus B \oplus M$$

Alice then xors in her original string $A$, and sends

$$A \oplus (A \oplus B \oplus M) = B \oplus M$$

Now, someone in the middle hearing these three exchanges, if they exclusive or all three, they get:

$$(A \oplus M) \oplus (A \oplus B \oplus M) \oplus (B \oplus M) = M$$