Changing your permalink would definitely fluctuate your site's SERP ranking for the next 1-2 weeks and I don't think there would be any exception.
Unless if absolutely necessary, I don't think you should change the permalink, if you are already enjoying good ranking in the SERP - you don't want jumping into a hot pan instead.
But if SERP ranking isn't the primary concern, you can definitely change the permalink anytime, and there are SEO plugins, which can help you redirect all traffic to the https version once implemented.