Both example sentences in the question are perfectly acceptably, even natural, in US English. I do not agree that (b) is "weaker" or that the current non-existence of the cake makes a difference. The true referent here is the task or project of making the cake.
This form can be used for both duties
The problem is yours to fix.
The money is yours to spend.
However I have heard it more often when imposing a duty than when recognizing a privilege.
This construction can be used with possessive pronouns other than "yours".
The choice is hers to make.
This carries the implication that it is hers and not yours, and can be used as a way of saying "don't interfere in someone else's choice."
The sofa is mine to given away or keep.
This is asserting a privilege, the right to make a decision.
The profits are mine to keep.
This is asserting ownership.
The situation is mine to deal with.
This is asserting a duty, perhaps a self-imposed one
The election is his to lose.
This carries a special implication. It means that the opponent cannot win if "he" does not make a mistake. Often the implication i9s that a mistake causing him to lose is seen as likely, or at least possible. A common varient is:
The game is theirs to lose.
about a sports event, implying that one team has an advantage and will win unless they make mistakes sufficient to give the game to the other side.