I rarely see canker on nectarines/peaches. In few instances I saw it, I prune the diseased branch and disinfect the wound with alcohol. As for grafting, just pick a dry day, and wrap the grafting site with parafilm down to 1” below the grafting wound. I have never seen a tree get infected with a disease from grafting, and I have done hundreds of grafts in my backyard.
FYI, bacterial canker is very common here with apricots, and to a lesser extent with plums and cherries. I have lost a dozen trees to bacterial canker.