第一. No smoking 不作無煙解。應作「不可吸煙」論。
第二. 你看過 Handle with care 這用法了。解作「應小心處理」吧!
我不以為 No 可以 with 為相對,但我認為意義接近;所不同的,就以文化差異去解釋了!
"Without you"是常見的歌詞,意思是 with you 的相對了;這裡的 with 和 without,也與有、冇同義。你會接受這解說嗎?
For "no smoking"'s opposite you can say "Smoking is allowed".
But there are many other answers to the question if you are not just talking about smoking. Will be great if you can further elaborate.