After some research… Is there a way to check equivalent BTC-ETH address without any privkey risk?
No there is no way, Eth address are a partial hash keccak of the public key.
A lot of people already said that sharing the hash sha256 of the public is a secure way to prove tha you know the private key, and that is correct.
double Sha256 hash, I don't know how sure it would be against brute force, when giving the hash256 of the public key directly by mistake.
It is a single hash.
Bitcoin use a double hash to generare the address (sha256 - rmd160) that is the so called double hash.
With only the sha256 hash we has half of the way to the address without compromise the public key.