Hi and thank you for your question. I am not clear at all about what the trailer has to do with this.
I truly want to help you but am totally confused on what the problem is.
It sounds like the bike is not running and you believe the ECU has failed. You ask about converting it to CDI. Even without knowing exactly what is going on here, that is not realistic. There are a multitude of problems with that, some of which I will touch on. The first issue is,your scooter is fuel injected (providing it is a genuine Yamaha Zuma 125) so if you could get rid of the stock ignition, you would also have to replace the fuel injection system with a carburetor. That would entail finding or making brackets, cables, manifolds, etc to actually make it work. It could also include jetting the carb so it actually runs properly as well. All of that is no small undertaking. Then, the next problem is, no one makes a replacement CDI for your bike. To find something to be able to adapt to your bike would be extremely time consuming because a lot of it is going to be trial and error testing and machining parts so they can be adapted and fit to your bike. By the time you got all that working, you would have so much time and money in it, you probably could have bought another scooter and saved yourself the trouble.
Now, if you can tell me what problem the scooter is having and why you don't want to fix what you have, we can go from there. When you explain it to me, keep in mind I have never seen your scooter or this trailer set up, so you have to be very specific. If the scooter has been modified to work in or with this trailer, tell me everything that was done to it as well. From what I know so far, it isn't even close as to what is the easiest solution is, fix the stock components. If I am missing something, that is what I need you to fill me in on.