Question: Can a smart contract execute a function of another contract on behalf of a wallet whose key it holds

Okay I'll try to write this more simply. Lets says Contract A has a private key of Wallet B stored in it. Contract A wants to call a function in Contract C on behalf of the Wallet, but for whatever reason, Contract C requires the msg.sender to be Wallet B.

Now if Contract A has the private key/mnemonic/ any required credential of wallet B, can contract A call Contract C such that it passes the msg.sender test.