I'm not suggesting blowing your nose into your sleeve or clearing some heavy phlegm from your lungs onto your cashmere, just catching any sudden public sneezes or coughs which for me don't normally produce that much mucus, just a little wetness on the sleeve. I've been doing this for years and it's fine, occasionally needing to go clean my arm or sleeve in the bathroom, which is better for not sharing viruses than getting it on your hands. You can also keep your mouth closed when coughing and swallow any mucus or go spit it into a toilet, not the floor.
Tissues or hankies are OK as long as you wash both hands thoroughly after each use or touch of a used one.