Bad news; your cream already contained a good dose of biocides to prevent it from growing bacteria when you stick your fingers in the jar. That should be sufficient.
The best antiseptic for spots and pimples, cat scratches and general small injuries is Corsodyl mouthwash. If you get a hot sore spot on your face, which you know is going to be a zit the next day, dab Corsodyl on it with a cotton bud. It will sting a little but the spot will be gone in the morning, headed off at the pass. The active in Corsodyl is chlorhexidine, which is used to prep people for operations.