If you’re just firing the URL to the default browser, I don’t know if you need ATS. However you’d wanna https it otherwise modern web browsers will baulk at it and that may lead to customers lacking confidence in your work.
Also consider if it’s just a single page, include it within your app. If you still wanna keep it on the server, make sure you use separate folders for different versions of the application.
I personally would investigate that as it is behaving the opposite of what I experience, and what I understand from the documentation. http should be the problematic one, not https.
All my products have the ability to show pages on our site via the default browser, and in some cases I even show web pages within the product (these pages have additional signing on them incase of a site level hack). I don’t do anything special to enable this, except use https.
It is entirely up to you how you do it, using version folders means you won’t be supplying version 2, 3, 4, 5, help to someone running version 1. Especially as you UI improves over time.