Let us assume we have a LIBOR 3M curve and that I would like to introduce a small shock up/down of 1bp at a certain point along the curve. I am trying to find out what the best and most efficient way is of doing this, but so far I haven't found a standard approach to be followed.

My yield curve is made of cubic splines, and so shifting a point up by 1bp might cause my curve to suffer from unrealistic/undesirable twists around the point in question, rendering the new curve useless.

A different approach I have thought of could be shifting up the point by 1bp and then perform linear interpolation in that local area. Thus, if we shift the point at t(i) and I have t(i-1) < t(i) < t(i+1), then I would do linear interpolation for the points between t(i-1) and t(i+1).

Has anyone had to solve this problem before? What would be the best approach without making the new curve look funny?