Insect brood parasites have evolved a variety of strategies to avoid being detected by their hosts. Few previous studies on cuckoo wasps (Hymenoptera: Chrysididae), which are natural enemies of solitary wasps and bees, have shown that chemical mimicry, i.e., the biosynthesis of cuticular hydrocarbons (CHC) that match the host profile, evolved in several species. However, mimicry was not detected in all investigated host-parasite pairs. The effect of host range as a second factor that may play a role in evolution of mimicry has been neglected, since all previous studies were carried out on host specialists and at nesting sites where only one host species occurred. Here we studied the cuckoo wasp Parnopes grandior, which attacks many digger wasp species of the genus Bembix (Hymenoptera: Crabronidae). Given its weak host specialization, P. grandior may either locally adapt by increasing mimicry precision to only one of the sympatric hosts or it may evolve chemical insignificance by reducing the CHC profile complexity and/or CHCs amounts. At a study site harbouring three host species, we found evidence for a weak but appreciable chemical deception strategy in P. grandior. Indeed, the CHC profile of P. grandior was more similar to all sympatric Bembix species than to a non-host wasp species belonging to the same tribe as Bembix. Furthermore, P. grandior CHC profile was equally distant to all the hosts’ CHC profiles, thus not pointing towards local adaptation of the CHC profile to one of the hosts’ profile. We conducted behavioural assays suggesting that such weak mimicry is sufficient to reduce host aggression, even in absence of an insignificance strategy, which was not detected. Hence, we finally concluded that host range may indeed play a role in shaping the level of chemical mimicry in cuckoo wasps.