I've never soldered my banana plugs and never had an issue. Your concern about the wire contact to the connector is unnecessary in this application. If you DO want to solder them, solder type bananas are available. Tinning keeps the wires from fraying, but other than that, offers no real benefit within a connector (and no downside either) other than the fact that if you are going to tin them, you don't really need connectors IMO. Connectors are no better or worse than bare wire. While there is some loss I'm sure, I'm going to say it will be nearly impossible to tell the difference.
Your wires are already tinned, so that means you don't have additional work to do it, though I still find Bananas far more convenient than having to screw/unscrew all of the binding posts on the speakers and receiver/amp and makes for a cleaner install in most cases.