Two antimicrobial agents such as silver nanoparticles (AgNPs) and titanium dioxide (TiO2) have been formulated with natural polysaccharides (chitosan or alginate) to develop innovative inks for the rapid, customizable, and extremely accurate manufacturing of 3D-printed scaffolds useful as dressings in the treatment of infected skin wounds. Suitable chemical–physical properties for the applicability of these innovative devices were demonstrated through the evaluation of water content (88–93%), mechanical strength (Young’s modulus 0.23–0.6 MPa), elasticity, and morphology. The antimicrobial tests performed against Staphylococcus aureus and Pseudomonas aeruginosa demonstrated the antimicrobial activities against Gram+ and Gram− bacteria of AgNPs and TiO2 agents embedded in the chitosan (CH) or alginate (ALG) macroporous 3D hydrogels (AgNPs MIC starting from 5 µg/mL). The biocompatibility of chitosan was widely demonstrated using cell viability tests and was higher than that observed for alginate. Constructs containing AgNPs at 10 µg/mL concentration level did not significantly alter cell viability as well as the presence of titanium dioxide; cytotoxicity towards human fibroblasts was observed starting with an AgNPs concentration of 100 µg/mL. In conclusions, the 3D-printed dressings developed here are cheap, highly defined, easy to manufacture and further apply in personalized antimicrobial medicine applications.