What you are describing is usually called "tinning" the connector pins.
It can make soldering to the pins easier, especially if you also tin the ends of the cable wires prior to inserting each wire into the connector pin. However if the connector pins are clean, the wire ends are clean, and your soldering iron tip is clean and has the proper temperature control, it may not be necessary for you to tin the pins in order to make a good connection. It's best to use really thin solder for this (it will easily melt and flow into a thin film on the surface).
Some DB-9 connector pins may already be tinned right from the manufacturer (in which case there may be no advantage to tinning them by yourself, although you may still want to tin the wire ends). Other types of DB-9s may have a gold or other surface which is not tinned by the manufacturer.
If you do decide to tin the connector pins, you need to add solder sparingly, however - too much will fill up the "cup" portion of the pin, which will make it difficult for you to insert the tip of the wire into the cup before applying heat (inserting the tip of the wire into the cup makes soldering easier because it adds some mechanical rigidity to the joint so that the tip of the soldering iron does not push the tip of the wire out of contact with the pin).
You also want to avoid inadvertently leaving whiskers or blobs of solder on the pins, which can also make it difficult to insert the wires, or can lead to pin-to-pin shorts. Ditto for tinning the wire ends - if you end up with a blob of solder at the tip, just cut off the blob with your diagonal cutters. Also, avoid overheating the wire ends which can melt back the insulation, which could lead to a later short circuit within the connector.
Also, avoid leaving unburned flux on the surface of any pins or wire ends that you tin. You may be able to burn it off when you make the soldered connection, but it is also possible that you will not, which could lead to a bad joint. Swabbing with isopropyl alcohol should remove any left-over flux residue.
The whole process will be faster than it took for you to read this...