One a spell or ability has had another player choose modes for it, a player can’t choose to not finish casting or activating that spell or ability unless there’s no way for the player to complete the process. For example, the player can’t choose to not activate mana abilities to pay for the spell.

While playing with your hand revealed, you can still reveal cards to pay a cost.

If you need to choose a card in your hand without revealing it to other players (most likely because an effect instructs each player to discard a card), you can hide your hand while choosing one or use any other method to keep your choice secret.