Every man, everyone period, should carry a handkerchief. I like the simple cotton bandannas sold at any discount store. I keep mine in my hip pocket. Emergency bandage, tourniquet, snot rag, restraint, sun hat, air/water filter, disguise, loincloth, potholder, etcetera. A 2-pack is less than $2. Online a common deal seems to be 12 for $10.

They get softer and more absorbent with a few washing and last for years.

I scarcely leave the house without a bandanna stuffed in a pocket neatly folded. Most of my commonly used jackets and coats have one in a pocket.

As for the bully situation, a lot depends on local standards. Often offering any resistance, any resistance at all, serves to cut the worse of it. A lot of determining the pecking order has to do with proving your a 'regular guy' and will fight if pushed. Winning is often beside the point.