Sometimes you can get away with placing a layer of paper and a few layers of tape on that to hold the ribbon cable in place well enough to make contact.
Ribbon connectors can be VERY difficult to desolder and solder without melting them. The old one can be removed with hot air (doesn't matter if it melts), but to solder the new one on, hot air is probably not recommended. Instead try a soldering station on a low setting, with a low melt solder like and just be quick with the iron and avoid touching the plastic. People seem to have more success that way. That advice isn't specifically for this ribbon connector but general advice, which should also apply to this. As in this case it's only 4 pins, it shouldn't be difficult to solder with an iron, you might not even need low melt solder, but it's an incredibly handy thing to have around for tricky soldering or desoldering jobs. Pricy though.
Edit: It keeps turning the Amazon link into an embed and the embed isn't working for me.
Code:
https://www.amazon.com/gp/product/B0019UZP7I/
So here is the link in a code block in case the embed is broken for you too.
Edit2: That daughterboard only has buttons and such on it, no logic, correct? You could probably buy a replacement daughterboard for a reasonable price (it might be the only way to get the ribbon connector anyways) and you wouldn't have to worry about soldering.