Replacing old concrete and stone step

[Daxbuddy]

We have a few outdoor steps to our yard that are made of old concrete (cement?) with large pieces of slate embedded. The thin bottom step is cracked and wobbly, so I'd like to replace it. The thicker steps seem very solid. They are shown on right side of pic.
The concrete is old (like, 70's old), pale and has a bit of exposed aggregate. I'd like to match it if I can.
Would appreciate suggestions on the "concrete" product to set the stone into, as I will chip out the old slate an re-use it. Our weather here is hot summer and cold winter, hoping to avoid freeze/thaw cracks. Hopefully not too specialized, as our local hardware store options are limited. I will dig out a few inches under the step to allow for 4-5 inches of concrete over a base layer of sand. The surface area is roughly a square yard.

Thanks

 

[AC Power]

Personally, I would use a hammer and a chisel...the old fashioned way. Today, many people are prone to look for portable power equipment to do it, but considering the sensitive nature in which the mortar needs to be removed (without cracking slate)., it might be your only option. Using a hammer drill to break up the larger pieces of concrete beneath the slate might be an idea, but the finer removal surrounding the slate, I'd use a hand chisel and a hammer......pretent to be an archeologist for the day!