What is the ethical way to go?
As part of your initial consultations, find out what are the expectations of the client. Are they expecting you to become their IT department while you're on the contract? Are they wanting lots of records about what you did and how long it took? In some cases, it may be worth discussing with a CFO if there are advantages to breaking things down one way or another.
Keep doing it as I'm doing?
I'd advocate having a conversation at the start that clears things in terms of how are things done and what works best for everyone. It may appear a lot like what you are doing now, but it may be better to know that this is what the client wanted.
Giving the shopping list to the client and let them deal with it?
This may work for some places where in the discussion they want to know what they are getting or record things in the books for themselves.
Are there laws about this kind of practice in places like the US or EU?
Consult a lawyer on this as I'm not a lawyer and wouldn't consider this legal advice in any way, shape or form. There could also be tax implications that make consulting a tax specialist also a good idea.