"Feline acne" is a term used loosely to describe what is presumably “black heads” on the chin of the cat. These black pimple like lesions are made of debris that builds up from the hair follicles and can sometimes result in bacterial infection. "Classic" feline acne appears to involve follicle plugging (comedones) in the chin and lip margin region. The cause of feline acne is not known. In that multiple cats in the same environment have been noted to develop feline acne at the same time, there has been some suggestion that an underlying viral etiology is possible. Although it seems to have a classic appearance, if it worsens or does not respond to therapy, other diagnoses should be considered such as bacterial or yeast infection on the skin that is usually secondary to allergies- either inhaled or food sensitivity. Mites and other allergic type and immune mediated problems should be considered as well as contact allergies such as to food or water bowls.
Assuming the simple case of feline acne, vets will often prescribe topical Mupirocin is available in ointment formulation (Bactoderm, Pfizer Animal Health) or you can try topical benzoyl peroxide cream or gel. Metrogel is another available topical treatment.
So, to answer your question, you can use peroxide, but it is not likely to make a big difference. Please see your vet to ensure the proper diagnosis and get some medications from them, ideally!