How to correctly solder the charging plug on my Bluetooth speaker?

The SOCKET, in the speaker, would be hard to come off. So, I assume you are talking about the PLUG from the adapter.

Those wires are prone to breaking. If there is enough left on the plug to work with, you can splice the wires. Just make sure you connect the same colors together. Normally, the + wire is the center of the plug. So, if the wires happen to be the same color you can meter the voltage from the adapter after cutting loose to get them correct.

The wires are usually very fine so it will be more difficult. Stagger the splice so you can use a piece of shrink sleeve over the whole thing without them shorting out. That way the splice won't be so big.