I've never had any fish injured on sharp edges of slate or any other rock - you use common sense choosing the pieces. Slate may not be natural to the east African lakes, but it is very useful for building the kind of artificial habitat we like for mbuna.
We have a weathered green limestone around here, interesting stuff because geologically, it fits with North Africa, as yet another relic of the tearing apart of the continents. It doesn't add a whole lot of hardness to my tanks. Tanks with it will creep up to pH 7.4, and so far, that's all.
If I use what around here is regular limestone, the pale grey version, it shoots the pH right up to 7.8, and would probably do more without water changes (my tap runs pH 6.6 to 6.8 at this time of year), but the green version hasn't been as active in the water.
I start with very soft tapwater, so I thought it would have a stronger effect. Grey limestone certainly does in my Mexican livebearer tank.