A timer is just fine, I don't use a cable too, but my camera has 2 timer settings, the default (10 secs iirc) and a short one (2 seconds) especially for these cases.
Although you can't really teach photography over the net, here are a few steps that might help you get instant improvment with your images:
1. Put your camera in "AV" mode
2. Set the iso to 100
3. Set the aperture to f/5.6 (2 stops down from your wide open f/2.
and let it set the shutter speed automatically.
4. Put the camera on a tripod
5. Compose your photo
6. Make sure your focus is correct
7. Shoot using a timer to avoid camera movement when you press the button.
You should see a big jump in quality in terms of sharpness, chromatic aberration and noise (although there isn't much difference between ISO 125 to ISO 100...)
Edit: I now see you don't have manual controls in your camera, that's a shame...
Perhaps the camera will choose a small aperture on macro mode, I suggest trying it instead of the missing "AV" mode (and skip #3 as you can't set your aperture)
