Background/Objectives: The increasing emergence of antimicrobial-resistant Staphylococcus pseudintermedius has limited the effectiveness of conventional therapies for canine pyoderma, highlighting the need for alternative topical strategies. This study aimed to develop hydrogels incorporating essential oils (EOs) from Peumo (Cryptocarya alba) and Tepa (Laureliopsis philippiana) as potential topical treatments against Staphylococcus pseudintermedius skin infections in veterinary medicine. Methods: EOs were obtained by steam distillation, chemically characterized by gas chromatography–mass spectrometry (GC–MS), and evaluated for antibacterial activity against S. pseudintermedius strains. Carbopol^®-based hydrogels incorporating the EOs of C. alba (HCA), L. philippiana (HLP), and a control vehicle (HVE) were formulated and characterized in terms of physicochemical properties, microbiological safety, and stability under accelerated and refrigerated conditions. Preclinical dermal safety was evaluated in BALB/c mice by repeated topical administration for five days. The analysis included clinical observation, skin irritation scoring, and histological analysis. Additionally, a preliminary microbiological evaluation was conducted in client-owned dogs with superficial pyoderma to assess the performance of the formulations in the target species. Skin lesion swabs were collected at baseline and after 21 days of treatment, followed by bacterial culture and automated identification using the VITEK^® system. Bacterial detection and bacterial load were evaluated to determine changes in microbiological status over the treatment period. Results: GC–MS analysis identified sabinene and eucalyptol as the main compounds in CA-EO, and linalool, eucalyptol, and safrole in L. philippiana EO. Both EOs exhibited moderate antibacterial activity against S. pseudintermedius (inhibition zones 4.9–10.8 mm; MIC ≥ 2.048 mg mL⁻¹). The hydrogels were microbiologically safe. Among formulations, HLP demonstrated superior physical stability and comparable rheological properties to the vehicle. In vivo safety evaluation demonstrated no signs of systemic toxicity, behavioral alterations, or skin irritation, and histological analysis confirmed preserved skin architecture without evidence of inflammation or tissue damage. In the preliminary microbiological evaluation in dogs, all animals were positive for Staphylococcus spp. at baseline. On Day 21, bacterial elimination was observed in the active treatment groups, but not in the HVE group, with elimination rates of 50.0% for Inveclor^® and 25.0% for both HCA and HLP. In parallel, HLP showed the highest proportion of dogs reaching minimal bacterial load levels (75%), followed by Inveclor^® (50.0%) and HCA (37.5%), whereas no dogs in the vehicle group reached this category. Conclusions: EOs from C. alba and L. philippiana presented antibacterial activity and were successfully incorporated into microbiologically safe hydrogel formulations. Notably, HLP demonstrated superior stability and a favorable preclinical safety profile, supporting its potential. In the preliminary microbiological evaluation in dogs, numerical differences in bacterial elimination and bacterial load categories were observed among groups; however, these differences were not statistically significant and should be interpreted as exploratory.