No. Not likely. Chromosomes contain our genes. Genes are the blueprints for the body including production of hormones.
I'm not saying changing sex chromosomes will never be possible, just that the hormone avenue is likely a no go. It would more likely more akin to rewriting gene code, so an editing process.
Trouble is, most genes have multiple functions so you can't just rewrite sections willynilly without taking that into account.
It's an intriguing idea though. It would be nice for people who chose to go through gender change could do so without or lessened surgical procedures/difficulties/complications.