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Single-chain nanoparticles (SCNPs) are a class of materials formed by the intramolecular cross-linking and collapse of single polymer chains. Because their morphology dictates suitability for specific applications, such as nanoscale reactors and drug delivery vehicles, understanding how to control or tailor morphologies is of interest. Here, we investigate how the morphology of SCNPs depends on both precursor chain attributes, such as linker fraction and backbone stiffness, and an imposed shear flow. Using coarse-grained molecular dynamics simulations, we generate an ensemble of structures from 10,800 unique SCNPs, some formed under quiescent conditions and some in shear flow--the latter of which has not been previously studied. We then characterize morphologies by analysis of a three-dimensional embedding space obtained through unsupervised learning of the simulated structures. This reveals how SCNP morphology depends on dimensionless parameters, related to precursor-chain attributes and shear rate, and offers insight into their relative influence. Interestingly, we find that shear rate has comparable influence to the degree of polymerization and the blockiness of reactive sites. Furthermore, shear, which can be externally controlled independent of precursor chain synthesis, can have persistent effects on morphology, such as enhancing compaction of SCNPs based on stiff chains. This work provides guidelines for designing SCNPs with targeted characteristics based on five dimensionless variables and illustrates the utility of machine learning in analyzing SCNPs formed across a range of conditions.