Can one develop a "chancre sore" appearance to a bump from shaving down south?

No the chancre. Has a hard edge, usually dry and painless. Caused by treponema palidum, sphylis. A chancroid is the same size, painful, oozes, soft edge. Caused by haemophilis ducreyei. Both are sti's. So yes, but not all are syphilis. The chancre goes away, but the disease persists. You cannot get it from shaving or toilet seats.