Although research on risk management (RM) in small-and medium-sized enterprises (SMEs) in general and regarding supply chains (SCs) has increased recently, our understanding is still rather fragmented and underdeveloped. This refers particularly to new types of risks such as dynamic crises or emerging risks associated with digital transformation (DT). Therefore, the purpose of this exploratory paper is to investigate RM in SMEs in SCs. More precisely, the aim is to identify patterns that can be used to group SMEs according to their risk behavior (i.e., risk attitude and perception). Drawing from a data set of 181 European SMEs, this paper empirically conceptualizes a typology of SMEs. The typology consists of four distinct types of SMEs that emerged from a cluster analysis: collective risk eliminators, collective playing it safe seekers, collective risk-ignoring knights of fortune, and collective neglecting imperturbable ones. The findings indicate that different risk behavior leads to different degrees of collaboration within the SC. Furthermore, the close interconnection between RM as found in the different clusters and the respective firm’s innovation performance can be shown. By acknowledging the heterogeneity found in SMEs, this paper breaks away from mainstream research that tends to consider SMEs as a homogeneous entity.