Analyzing future weak lensing data sets from KIDS , DES , LSST , Euclid , WFIRST requires precise predictions for the weak lensing measures . In this paper we present a weak lensing prediction code based on the Coyote Universe emulator . The Coyote Universe emulator predicts the ( non-linear ) power spectrum of density fluctuations ( P _ { \delta } ) to high accuracy for k \in [ 0.002 ; 3.4 ] \mathrm { h / Mpc } within the redshift interval z \in [ 0 ; 1 ] , outside this regime we extend P _ { \delta } using a modified Halofit code . This pipeline is used to calculate various second-order cosmic shear statistics , e.g. , shear power spectrum , shear-shear correlation function , ring statistics and COSEBIs ( Complete Orthogonal Set of EB-mode Integrals ) , and we examine how the upper limit in k ( and z ) to which P _ { \delta } is known , impacts on these statistics . For example , we find that k _ { \mathrm { max } } \sim 8 \mathrm { h / Mpc } causes a bias in the shear power spectrum at \ell \sim 4000 that is comparable to the statistical errors ( intrinsic shape-noise and cosmic variance ) of a DES-like survey , whereas for LSST-like errors k _ { \mathrm { max } } \sim 15 \mathrm { h / Mpc } is needed to limit the bias at \ell \sim 4000 . For the most recently developed second-order shear statistics , the COSEBIs , we find that 9 modes can be calculated accurately knowing P _ { \delta } to k _ { \mathrm { max } } = 10 \mathrm { h / Mpc } . The COSEBIs allow for an EB-mode decomposition using a shear-shear correlation function measured over a finite range , thereby avoiding any EB-mode mixing due to finite survey size . We perform a detailed study in a 5-dimensional parameter space in order to examine whether all cosmological information is captured by these 9 modes with the result that already 7-8 modes are sufficient .