Shaving or scraping back concrete

[Nozzle]

So I have a thin strip of concrete forming a part of my floor upstairs. I'm planning a job to do some re-flooring (as shown on the photo to the left, it's all chipboard and creaky - to be replaced with floorboards). There's very little chance the new floorboards will be exactly the same thickness as the old chipboard so to keep the floor even I'm going to have to alter the form of the concrete strip.

Is there a tool or similar I can use to scrape or shave back the top of the surface either deep enough to lay the boards over, or just to bring it flush again. I have an angle grinder but that produces a huge amount of dust and I need to keep that to a minimum to save the decor/carpet. And it wouldn't be a particularly flat job.

Once shaved back, or if the new flooring sits proud, is there some kind of runny concrete/screed/backfill I can use to bring it back flush again?

Nozzle

 

[ladylola]

The tool to use would be an angle grinder fitted with a spinner or diamond cup wheel
http://t.homedepot.com/p/RIDGID-4-in-Double-Row-Diamond-Cup-Wheel-HD-AWD40/202884364
However , that does produce quite a bit of dust so the only real answer is a simple carbo block and elbow grease ,
http://www.greenham.com/c/pl/139449/Professional-Carborundum-Block-(Plain)

The links are just the first ones I come across for illustration rather than a recommendation of which ones to actually buy.

 

[Nozzle]

Thanks Ladylola for the links. That little block is exactly what I'm after, perfect!

Nozzle