though the jurisdiction wasn't mentioned, nearly everywhere it is illegal to manage the funds of others for trading unless registered to do so (e.g., as a brokerage or as a qualified custodian)
looking back at your question, you aren't asking the intermediary to invest for you so that person isn't really managing your funds. instead you are probably simply looking for someone else to buy some shares, sell them to you (for btcs) and to then transfer those shares to your account.
there are people who deal with cash only and no bank account. a family member or friend helping another by providing this assistance (as a favor, not for profit as a business) probably can do so without any interference. keep in mind though no part of the transaction will be private as the brokerage doing the transfer will need to report the account that the shares came from.
