Hepatitis B virus (HBV) infection remains a major health threat with limited treatment options. One of various new antiviral strategies is based on a fusion of Staphylococcus aureus nuclease (SN) with the capsid-forming HBV core protein (HBc), termed coreSN. Through co-assembly with wild-type HBc-subunits, the fusion protein is incorporated into HBV nucleocapsids, targeting the nuclease to the encapsidated viral genome. However, coreSN expression was based on transfection of a plasmid vector. Here, we explored whether introducing protein transduction domains (PTDs) into a fluorescent coreSN model could confer cell-penetrating properties for direct protein delivery into cells. Four PTDs were inserted into two different positions of the HBc sequence, comprising the amphiphilic translocation motif (TLM) derived from the HBV surface protein PreS2 domain and three basic PTDs derived from the Tat protein of human immunodeficiency virus-1 (HIV-1), namely Tat4, NP, and NS. To directly monitor the interaction with cells, the SN in coreSN was replaced with the green fluorescent protein (GFP). The fusion proteins were expressed in E. coli, and binding to and potential uptake by human cells was examined through flow cytometry and fluorescence microscopy. The data indicate PTD-dependent interactions with the cells, with evidence of uptake in particular for the basic PTDs. Uptake was enhanced by a triplicated Simian virus 40 (SV40) large T antigen nuclear localization signal (NLS). Interestingly, the basic C terminal domain of the HBV core protein was found to function as a novel PTD. Hence, further developing cell-permeable viral capsid protein fusions appears worthwhile.