In recent years, several laboratory studies of CNO cycle-related nuclear reactions have been carried out. Nevertheless, extant models of stellar nucleosynthesis still adopt CNO reaction rates reported in old compilations, such as NACRE or CF88. In order to update these rates, we performed new calculations based on a Monte Carlo R-Matrix analysis. In more detail, a method was developed that is based on the collection of all the available data, including recent low-energy measurements obtained by the LUNA collaboration in the reduced background environment of the INFN-LNGS underground laboratory, on R-Matrix cross-section calculations with the AZURE2 code and on uncertainty evaluations with a Monte Carlo analysis. As a first scientific benchmark case, the reactions 17O(p,γ)18F and 17O(p,α)14N were investigated. Among the different stellar scenarios they can influence, the 16O/17O abundance ratio in RGB and AGB stars is the one that can be directly confirmed from spectroscopic measurements. The aim is to reduce the nuclear physics uncertainties, thus providing a useful tool to constrain deep mixing processes eventually taking place in these stars. In this work, we present the procedure we followed to calculate the 17O(p,γ)18F and the 17O(p,α)14N reaction stellar rates and preliminary comparisons with similar rates reported in widely used nuclear physics libraries are discussed.