I am thinking is there a way by which I can create a blur effect by using the light wind in my favor?
There are a lot of possibilities. Some examples:
Use a long shutter speed -- several seconds or more -- so that the moving flowers blur into soft shapes and stationary objects like a fence or statue stay sharp. The effect will be like photos you often see of water flowing in a stream, giving a sense of movement and stability at the same time.
Combine motion-freezing flash with ambient light to give an image where the flowers are sharp but also have a "ghost" effect around them. Second-curtain sync may work best here.
Overpower the ambient light with flash, but have the flash fire several times during the exposure. If the flowers are moving, each one will appear in as many positions as there were flash pops. Moving objects will look translucent in some places and more opaque in others (where they overlap), and stationary object will look more solid. If you're having a hard time overpowering the ambient light, shoot in the evening or even at night.
This should not look as if there is a hand shake. Mind it that the wind is quite light.
The best way to avoid camera shake is to use a sturdy tripod or other fixture. Don't try to hand-hold the camera while trying to use a long enough exposure to capture flower movement -- you can't hold the camera steady that long.
Will using a macro lens provide a special benefit in this case?
Only in that you can, as always, take close-up photos of small subjects. The small motions of flowers in a gentle breeze will look relatively large in a macro shot. Using a higher shutter speed when working close up will help limit the motion.
I have the 60mm macro lens which I am unable to use, ever, because of the light wind blowing in the garden
Even if the garden is your preferred subject, consider using that lens in other places, like indoors, where the wind isn't a factor. Lots of things are interesting at the macro level, and as you use the lens more you'll build experience that'll help you in more difficult situations, such as in the breezy garden.