In cases, linear interpolation was overpredicting the data and the actual formulae have powers of it this coeff, so it introduced error. Hence I decided to go for spline. But in a a ramge of Reynolds numbers near 1e5, I have observed negative values of the coeff, which are the artifacts of oscillation of splines (going below X axis) as you mention. And I don't have more data to in that section to "discipline" the spline, hence the switch to linear interpolation.
Depending on the actual formula it may be an option to use approximation instead of interpolation. Depends upon your knowledge about which kind of function you expect for a constant f resp. a constant Re. Would make the table lookup routine more complicated of course.