Its possible like Octavian did he won't engage in official hereditary succession but designate the successor he feels is best suited. That cuts down on charges of Eastern despotism and also there is the issue that while in his middle 50's Caesar could easily go on another decade or even more. By then Caesarion (as OTL) will probably be at least co Pharaoh of Egypt and him then being promoted to Emperor is liable to see people thinking his Mum is pulling the strings. Given the affair doesn't seem to have been that popular that could lead to issues.This is a fascinating take.
While I'm of the school that Caesar didn't really want to be king any more than he really knew how to fix Rome's ills (evidenced by his attempt to adjust the Republic into something that could govern the empire, instead of slowly creating something new ala Augustus), I could see him still coming around to the idea.
After all, what's to stop him from thinking Roman senators killed their kings. Then, Roman senators tried to kill me even when I wasn't a king. It's not kingship that's the problem here, is it? That - plus a growing disregard for the Republic institutions that have failed him time and time again - could push him right into the purple.
You think Octavian fancies being a prince, or is Caesarion getting the nod?
Also Cleopatra isn't going to be that young by then and Caesar may have set her aside if her looks have gone in her 30's...