IMHO.....no need to disinfect as the bacteria dies once exposed to air/dryness for like 24-48 hrs. To be totally safe; just leave it hang for a week! Wipe it off to make yourself feel better.
Ask your vet their recommendation too. And a less irritating disinfectant might be a chlorhexadine type like Nolvasan. Diluted.
A bleach disinfectant would be a 1:100 dilution if you wanna use that.
Or use a weak Nolvasan on your tack or......just soap & water!
Time from exposure is the key; it's more likely spread by the humans on their hands/clothes than anything.