Replacing Hybrid tyre
You can generally go down in tyre width without a problem because frame clearance is not affected.

Going up to larger sizes needs more careful checking, but down is mostly fine. 

Do note your rim does not have a "1.75" measurement anywhere.  Its more likely to be 20-25 millimetres in width across where the tyre seats to the rim 

One possible risk is decreasing tyre width can expose your rim to damage from potholes and kerbs, but this would be at about half the tyre size, and you're not near that.