It is somewhat of a delicate dance. Basically I strip enough wire so that there is a good amount exposed wire to set the iron on so that the heat is applied directly to the wire, not the pin. I use my Hakko 936 with the stock screwdriver type tip, it's a tight fit in there but I've been able to do it without melting the connector so far. I then flow just a bit of solder to allow some conduction between the wire and pin and then apply a bit more solder to facilitate the connection. That all takes about 3 seconds I'd say, if it starts taking longer I stop and wait for things to cool down before trying again. It usually works the first time and I haven't had it take more than 2 to get a good connection. I also then fill the remaining cavity in the Cardas connector with hot glue to try and take as much strain off of the soldered connection as possible. I also use a layer of adhesive-lined heat shrink between the connector's strain relief and the exposed wires with the same idea in mind. Then I wrap the whole business in on final layer of non-adhesive shrink to finish it off.
Bottom line, it's really not that hard but you do have to have the right tools and supplies.