Please next time include a scan or reference of the card in question.
To answer your question, you are correct saying you can't use cosmic power if you have zero cards in your hand. You have to have at least one card in your hand to use the power.
When it comes to cards involving public knowledge (I.e. Hand size, deck size, cards in discard pile, etc...) you have to do as much of the card text as possible. So for cosmic power, it reads "put up to two cards from your hand" this means you have to put at least one back to activate the power. Cards like looker's investigation read "shuffle your hand into your deck and draw up to five" meaning you have to draw at least one.
This is different for cards that don't involve public knowledge (I.e. What cards are in your hand or what cards are in your deck). That's why attacks like call for family can fail. It may say search your deck for up to two basics. It can fail because your opponent doesn't know what's in your deck. Or like Pokemon collector says search your deck for up to three basic Pokemon and put them into your hand. You can fail that and get 0 because it's not public knowledge.