  We derive exact traversable wormhole solutions in the framework of $f(R)$
gravity with no exotic matter and with stable conditions over the geometric
fluid entering the throat. For this purpose, we propose power-law $f(R)$ models
and two possible approaches for the shape function $b(r)/r$. The first approach
makes use of an inverse power law function, namely $b(r)/r\sim r^{-1-\beta}$.
The second one adopts Pad\'e approximants, used to characterize the shape
function in a model-independent way. We single out the $P(0,1)$ approximant
where the fluid perturbations are negligible within the throat, if the sound
speed vanishes at $r=r_0$. The former guarantees an overall stability of the
geometrical fluid into the wormhole. Finally we get suitable bounds over the
parameters of the model for the above discussed cases. In conclusion, we find
that small deviations from General Relativity give stable solutions.
