Puckishly is the adverb of puckish: you do something in a playfully teasing way, as if you are amused by other people and cannot resist a small joke at their expense. He smiled puckishly means the smile carried that private, stirring humour — light, not mean. Like puckish, it comes from Puck the fairy, not from the hockey puck, and it is a little literary. In speech, cheekily does much the same job with simpler clothes.