the RC-HD1 is designed for hd598... there's some locking mechanism. does the ATH have the same locking feature? if it's just straight plug in/out one, can check out the RC-MH1 instead.
btw just my imo on these fiio cables. they are made of pcocc-a. i have some of these fiio and oyaide cables. whether it's an improvement or not, gotta depends on what headphones the cable is used on and personal preference. imo such cables tighten up the bass, gives a faster and snappier feel but makes the overall sound leaner and more clinical, or harsher. so depends on what headphones they are paired with.
i tried with hd600 (oyaide hpc-62hdx), hd650 (oyaide hpc-62hdx)), hd25-1 ii (oyaide hpc-hd25), akg k702anni (oyaide hpc-x62), focal spirit one (fiio mh1), spirit classic (fiio mh1) and ue6000 (fiio mh1). worked great with hd650, hd25-1 ii, k702anni and ue6000 but didn't like it over the stock cable with the other three. was especially quite horrible with the spirit classic lol.
haven't heard the m40x nor m50x but just based on my impression with m50, if they are anywhere similar, i think it won't be a nice match. but yeah, that's based on my taste. ymmv so @newstranger, just go try it