I get a kick out of little crossword puzzles, and for clues like 'Japanese martial art' I lean on a mental toolkit of synonyms and alternate spellings. Short, common fills are things like judo, karate, kendo, aikido, and sumo — those are crossword staples because they fit many grids. If the clue is looking for a more umbrella term, budo or bujutsu can show up, and 'ryu' (meaning 'school' or 'style') is a sneaky short fill.
I also watch for variant spellings: jujitsu vs jujutsu vs jiujitsu, kenjutsu vs kenjitsu, and even 'iaido' sometimes appears when the clue hints at drawing a sword. For cryptic-style clues, think of action-based hints — 'sword art' for kendo, 'bow art' for kyudo, 'wrestling' for sumo, and 'throws' for judo. When crossings are sparse, consider short synonyms like 'fight art', 'combat art', or simply 'dojo' if the clue is punny. I always try the transliterations and the umbrella words first; they save time and often fit the grid, which keeps me smiling.