Recommended Post-op Care After Mole Removal?

I do not recommend hydrogen peroxide as it is quite irritating and tissue toxic. I advise patients to wash their faces and shower normally the day after surgery, gently dabbing the area dry afterwards. I then recommend a light application of vaseline twice daily as the shave excision site heals over the next week or so. Sunscreen is also important to protect the surgical site from UV exposure for one year post-operatively as the scar fades.

I Don't recommend using hydrogen peroxide, it's irritating and toxic to cells. I tell my patients to wash normally with soap and water then apply simple moisturising creams. If I'm worried about hypertrophic scar (lumpy scars) I prescribe them silicon gel or sheets. 

You are on the mark…too much moisture (i.e. neosporin in this case) and hydrogen peroxide will definitely delay wound healing. Just think about getting a cut and leaving it under water all the time.Wait until you have some wound healing. The Scar gels and creams come more into play for scar formation, not wound healing. They do help, but aren't necessarily worth a great financial investment if things are progressing normally.