Is it safe to charge my phone this way?

I have a Samsung galaxy 3, the charging port on it is distorted inside somehow.I've tried a few online repair tips but they don't work, the tongue inside the port isn't making good contact with the female part in the cable. Not when I use the factory cable anyway.

my solution was to try a bunch of aftermarket cables in the hopes that one of them was made too big on the outside/ or too small on the inside and by accident make good contact. It worked. I can charge my phone through my computers usb port… Its slow, but it works.

My question is: I still have the factory travel adapter main head that plugs into an outlet… Can I plug any old usb cable into it and charge my phone through an outlet again? Won't the factory plug in adapter regulate how much power the phone is getting? I found another aftermarket cable that works, rated at 2.4 amps… I don't think my phone can handle that. But if its plugged into the factory head it shouldn't get that much right?

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