That is a good connector. If you don't want to get a third hand or have a vice, then you could probably get by using mounting putty. Something like blu-tack, handitak or any of several other brands. It can usually be found in home improvement/hardware stores or office supply stores. It won't be a firm hold, but it should be good enough. You can clean off any residue from the putty with lighter fluid or mineral spirits.
The black solder joints suggest that the wire or connector has oxidized. I'll let those more knowledgeable guide you on to clean the wire and connector.
