welcome to health care magic and
thanks for posting your query
You do not have to be worried. true there is transmission of tetanus
through blades but only contaminated blade or old blades from the ground could do that.
You did used a new blade so all the troubles of infection from the blade are eliminated. However, the skin especially around the genital area habours bacterial which could infect a wound. But then you described the wound as a small wound that bled just for a while then stop.
You should clean regularly with soap and clean water and it will be ok.
Best regards and hope this helps.