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No. The rule you quote (and its equivalent for graveyards) is the appropriate one and mentions nothing about delays. The choice must be made immediately, but can be remade whenever the commander changes zones. For example, if you allow your commander to go to the graveyard, and then a card is played to exile your graveyard, you can once again choose to send your commander to the command zone instead. Once your commander has arrived somewhere (exile, graveyard), it stays there until a card tells it to move.

For completeness, the graveyard rule:

903.11. If a commander would be put into its owner’s graveyard from anywhere, that player may put it into the command zone instead.