Which wallet does not require verification?

I'm looking for a wallet that allows me to store my cryptocurrencies without the need for any form of verification. Could you please explain to me which wallets currently on the market offer this feature? I'm particularly interested in knowing if there are any reputable, secure options that don't require any identification or verification process during setup or usage. Additionally, I'd like to understand the potential risks and drawbacks of using such a wallet, if any.