3x3 LED Matrix with less pins
Option #2 can definitely work, it is based on a widely adopted side effect of human vision called Persistence Of Vision, abbreviated with POV, which is used in Television, LED cubes and many other display devices.

You SHOULD notice no flickering if you manage to keep a refresh rate above 24 FPS (Frames Per Seconds or full refreshes), but not all human being are the same, that's why we tend to aim at 60 or 100 FPS to ensure flickering is not perceivable by anybody.

What you WILL notice though is a reduced brightness as each LED will be turned on only for a fraction of time.

So, naming your pins as COL1 to COL3 and ROW1 to ROW3, you can refer to the following schematic:







simulate this circuit &ndash; Schematic created using CircuitLab

You can further extend your option #2 by using an external IC, commonly referred as LED drivers: not something you need unless you get short of outputs.