Yeah, I do not recommend using Deliveries as the default app for e.g. Amazon links due to the issues you described. Unfortunately, the system that allows my app to receive such links is very limited so I can't do a better differentiation of links (e.g. only offer Deliveries as option if the link is *amazon.com but also require something like "&trackingid=...").
The only workaround I could come up with would be to add an option to Deliveries that automatically opens the browser for links without a tracking ID instead of asking first. While probably not too nice visually and performance-wise, it would at least take the additional button press from you.
Unfortunately, I currently do not have the time to implement this but I added it to the "nice to have" list.