The CDPP propagation tool is used to propagate interplanetary coronal mass ejections (ICMEs) observed at Mercury by MESSENGER to various targets in the inner solar system (VEX, ACE, STEREO-A and B). The deceleration of ICME shock fronts between the orbit of Mercury and 1 AU is studied on the basis of a large dataset. We focus on the interplanetary medium far from the solor corona, to avoid the region where ICME propagation modifications in velocity and direction are the most drastic. Starting with a catalog of 61 ICMEs recorded by MESSENGER, the propagation tool predicts 36 ICME impacts with targets. ICME in situ signatures are investigated close to predicted encounter times based on velocities estimated at MESSENGER and on the default propagation tool velocity (500 km s−1). ICMEs are observed at the targets in 26 cases and interplanetary shocks (not followed by magnetic ejecta) in two cases. Comparing transit velocities between the Sun and MESSENGER ($ {\bar{v}}_{\mathrm{SunMess}}$) and between MESSENGER and the targets ($ {\bar{v}}_{\mathrm{MessTar}}$), we find an average deceleration of 170 km s−1 (28 cases). Comparing $ {\bar{v}}_{\mathrm{MessTar}}$ to the velocities at the targets (v
Tar), average ICME deceleration is about 160 km s−1 (13 cases). Our results show that the ICME shock deceleration is significant beyond Mercury’s orbit. ICME shock arrival times are predicted with an average accuracy of about six hours with a standard deviation of eleven hours. Focusing on two ICMEs detected first at MESSENGER and later on by two targets illustrates our results and the variability in ICME propagations. The shock velocity of an ICME observed at MESSENGER, then at VEX and finally at STEREO-B decreases all the way. Predicting arrivals of potentially effective ICMEs is an important space weather issue. The CDPP propagation tool, in association with in situ measurements between the Sun and the Earth, can permit to update alert status of such arrivals.