Well:
1) He never changes key signature, and the main theme is in major, from the strart, repeated several times.
2) It is idiomatic for Chopin to use that final chord progression. Look no further than Op. 32, No. 2. That ends on Db minor, so he likes a sort of minor IV chord to I, in a major key. He seems to reserve ending in minor for something big, such as the F Major Ballade, where his minor ending follows a ferocious coda in minor
3) A Picardi third is generally the final chord of something that starts in minor. Very typical in Bach, for instance. I would not call this a Picardi 3rd. I would call it simply a confirmation of all that went BEFORE the cadenza.
4) The cadenza is unexpected, a moood change, not a modulation that leads to parallel minor.
Of course it's all opinion, no proof, but *I* would suspect that he wrote a sharp to make it clear, that after all those previous D naturals in the cadenza.
But I'm open to counter-arguments. Mikuli shows D#, and I always give great weight to his edits because he actually studied with Chopin. Paderewski obviously did not.
