First of all I would like to precise what my species of wyverns actually are. I do not plan to make them huge and gigantic like in many fantasy worlds. Instead they are rather small and can be the size of a cat at most. And they do not breathe fire as they are part of a rather realistic futuristic Earth. These wyverns live relatively around the world (mainly in Antarctica) 100 million years in the future (Antarctica drifted towards the equator and got some of its rainforests back)
I would also like to note that humans no longer exist, thus any future evolution is not caused by humans.
Wyverns could potentially exist as a few traits like large leathery wings and the simple idea of a large flying creature has already been seen in nature. However these wyverns, being reptiles after all, have to evolve a few traits that would separate them from other reptiles before becoming a flying creature.
If I understood correctly, evolution is not really that hazardous. It depends on the environment and heavily influences natural selection. For example whales "returned" to the sea because of the opening of a new "niche" with vast nutritional resources, thus the early cetacean ancestors swam back into the sea and evolved into whales, dolphins etc.
In 100 million years many modern animals went extinct (such as most land mammals, birds, virtually all marine mammals, most shark species, turtles etc.) due to the "Sixth extinction" (I'm not gonna bramble about humanity being the cause or something else). And now begs the question.
Since my wyverns are descendent from modern reptiles, and replace the niche left open by extinct predatory birds (eagles, falcon etc.) in this scenario, how can wyverns evolve? Can large reptile species like monitor lizards be the likely ancestor of these wyverns? And what would drive them to "take to the skies", to maybe fill up the niche left open by predatory birds?