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Try and count the number of turns that are engaged that should give you a good idea of what thread length is actually engaged. The axle on the picture says 15mm thread length, so 10 turns of a 1.5mm thread pitch until it bottoms out. The 166mm axle has 17mm of thread length, so effectively the last thread sits 4mm further out than on the 160mm. If you have less than 7 turns to fully tighten the current axle, you should be able to use the 166mm if it makes you feel better. (Assuming the dropout isn't closed and the axle won't poke out too far. )
Try a wolfaxle a extra 7 mm !!!!!
https://www.wolftoothcomponents.com/search?q=wolf+tooth+rear+axle