I use an A* algorithm to find a path voiding obstacles. On obtaining the path it would be a good idea to reduce the number of points. Then I would like to typically do a spline interpolation or Bezier Curves to find a smooth path but is it not possible that post smoothening my character bumps into an obstacle? If not possible then why and if it is possible, then how do I avoid it?
Do as we all do: play with splines running between adjacent path cells, and see how it works. This is really totally down to personal interpretation. Then adapt your parameters from there. The primary issue is moving around corners. If the curve is too gradual, such that the entity bumps into inner corners during its arc, then strengthen the control point (move it outward) on the outer edge of the arc; this will sharpen the corner to some degree. OTOH, If the curve is too sharp, you're not much better off than where you are at the moment, and you probably need to move the control point back inward.
You can slightly bevel the corners of walls in your game, if all you are worried about is how this looks.
TL;DR Experiment and Adapt. That's a large part of the fun of game development.