There will be few rapidly-dividing cells in a fresh wound (which is the wound to which H2O2 is applied). In general, it is a good idea to avoid applying irritants to rapidly dividing tissue.
Hydrogen peroxide is a weak mutagen. It is produced in many body tissues, ingested in drinks, produced by mouth bacteria, etc. It may well cause some cancers. Some OSHA-mandated literature does warn that it is a mutagen and must be handled with care, but these are warnings to people who work with concentrated solutions.
However, a relatively weak hydrogen peroxide solution, even if it is mutagenic, would need to be left in place and active (or renewed) for a long period of time to produce skin cancer. 225
As it has been a staple of first aid kits for decades, and this association has never been made clinically, my best guess is that the benefit (as a bacterocidal agent) far outweighs the risk in the treatment of minor wounds. As in all things, however, prudence is advised. (I myself don't use it because soap and a lot of water is quite effective. Nor is it used in the care of wounds in Emergency Rooms where it is considered to be detrimental to wound healing. If I were in a country where clean water and soap were in short supply, I might well use it if necessary.)
Because it is an irritant (and many irritants can be considered mutagenic), it is actually used to treat precancerous skin lesions, the finding being that it affects the more rapidly dividing pre-cancerous cells than the rest of the epithelium.
Far more potent peroxides have been used topically, which may increase the risk of skin cancer.
Interestingly, one of the responses of skin cells to H2O2 is the generation of an oxygenase to fight the effects.
Topical sulindac combined with hydrogen peroxide in the treatment of actinic keratoses
Effects of Peroxides on Rodent Skin: Epidermal Hyperplasia and Tumor Promotion
Heme oxygenase is the major 32-kDa stress protein induced in human skin fibroblasts by UVA radiation, hydrogen peroxide, and sodium arsenite
Recent Advances in Wound Care, <PERSON>, <PERSON>, MS, and <PERSON>, MD 938