The notation is quite clear; play the d flat left and the b flat right. Of course, often the division between the staves doesn’t say much about division between the hands, but in the case of Chopin (who was an excellent pianist himself) and in the case of this study, it is clear what is meant.
But should you do it? You are always free to choose a different fingering from what the music seems to imply. If it is easier for you to switch the notes: by all means! You are not contractually bound to play everything exactly as written. However, when making this kind of changes pay attention that it doesn’t affect how the passage sounds.
A last aspect is that this is a study, in which you sometimes have to go with an inconvenient or impractical fingering because that is what the etude is about. In this case I would say that Chopin intended the crossing of the hands, since that fits nicely with the technical theme of the study.
In conclusion: I think Chopin meant for the hands to cross. I think it’s perfectly possible and I would just do it, but if it is very inconvenient for you or you prefer to uncross the hands here for some other reason there is nothing that says you can’t do that.