I think there is a possible future where "I" am a talking cucumber, though?

Ignoring that you have to give up a sense of personal identity at this point, there is nothing in the laws of physics that says the matter that makes up what we're presently calling me can't morph into a talking cucumber with a brain with my memories in it. It's just absurd number of extremely specific things that have to happen out of an ever more absurd number of possible things to happen.

Indeed such a strange configuration of matter would arguably no longer be "you", but I think an even more immediate point of philosophical incoherence is that it would certainly not be a cucumber. [Cucumber != cucumber] => false, QED.

If talking cucumber was too pedestrian for you, we could add stipulations until your intuition collapses. Perhaps, starting next week, the Earth begins to spontaneously turn into raspberry custard on Tuesdays. Perhaps the entire universe turns to custard! Just think of it - billions of lightyears of custard in every direction. Whoops, did I say billions? Too grounded! Let's make it a googolplex. And a single lone piece of rhubarb, floating somewhere in the middle of it all...

...sorry, couldn't resist. Joking aside, while we can quibble about the boundaries of the possible, the fact remains that there are boundaries - at least, if we're still talking about known physics. No evolution of the universal wave function will lead to a world where pi suddenly equals 3.