The approach I would take would be to lay a pressure treated 2x4 flat on each side of surface of the sidewalk and one on edge on each side that would hold everything in place without having to nail to the concrete or maybe only in a few places. If you want a 1.5" overhang, or cantilever, that would make the overall width 37" (which may be too wide for you). I would then screw 5/4 x 6" pressure treated deck boards to the 2x4's.
With this type of construction, you could even make it in say, 8' sections with the deck boards overlapping to fasten it together, and you would be able to lift the sections to clean debris underneath if necessary.

Sounds like a cool idea. I these kind of things always get my brain going. I hope you post pictures when you are done. My first thought was to ditch the plug idea. The whole thing will weather, you will have to occasionally replace a board and the plugs wil either be a royal pain to get up if you have glued them in, or if you don't, they wil be constantly popping out when you sweep. Furnone's suggestion made me think about the screw issue. If you do make it into 8' sections, you could build it "upside down" screwing from the bottom, then flip it over to the right side when done.

Thank you all, I do like the Furnone's approach, -removable/lifting sections-, still need to figure out how to make sure that rain water drains properly and how to "nail" the sections to the concrete so they are not loose when walking/standing on it and at the same time making them easy to remove (usage of hingeÂ).

dainaadele, nice idea to build it "upside down" screwing from the bottomÂ..for sure I will post pictures of the entire project, and also from my last one completed (trellis shade shelter).

Again thanks for your ideasÂyou know sometimes we get lost when looking for ideas, even making them so harder/complicated loosing sight of easy/simple solutions, someone on another forum suggest me to tear out the entire concrete sidewalk , but it doesnÂt make sense to spend money there as its in a perfect condition, only 2 years old. I am just trying to add a nice touch to my patio.

It is warm and sunny here in Madison, with a pleasant breeze. No reason for me to sound like a grinch, except for the concept of wood over concrete, in an exterior location. You can certainly put down wood over concrete in a building interior, this is done routinely when gymnasium floors are constructed. Wood over concrete in an exterior location is another matter entirely. Every time it rains, water will tend to accumulate on the concrete, and soak into the wood. Even pressure treated wood will tend to rot prematurely in this environment. Unless you live where it rarely rains, you can reasonably expect to be replacing the wooden sidewalk every 10 years or so.