[type0]

It would be interesting if there was a soldering iron with a thumb operated lever that will feed the tip with solder.

But heres some techniques:

Twist the wires together to make them stick. And then use the soldering iron to heat the joints and apply the solder. Maybe cover the tip of the iron with some solder to help with the heat transfer.

It's also a good idea to prepare the copper wires before you start soldering. By just adding a slight bit of solder into it. Then you know exactly when to apply the solder.

People tend to say that a powerfull iron can cause problems. But I would say the other way around. Using an underpowered soldering iron will cause you to use much more time to get the joints up to the right temperature. And maybe burn some other components meanwhile as copper is a good heat conductor. A powerfull soldering iron will heat up the joints much faster before the heat has time to escape elsewhere and do any damage.

Low power iron: "Heating the copper... waiting.... waiting... almost there... waiting... waiting... oh no! I burned the cap!"
High power iron: "Heating the copper.... that's it. Applying solder. Done"

And don't use too much solder. Use just about enough to saturate the joints in solder or you can easily end up having your whole work piece looking like the end shot of a bad porno.