Does anyone use 1/16-inch cable in either 7x7 or 1x19 configuration for fox?

Yes in 1x19.

I've caught fox in 1/16" 7x7 as well as 1x19 and 5/64" 7x7 it all will work fine my favorite is still 7x7 in either 1/16 or 5/64 but as I've said before try it all and see what works best for you .
In all honesty this is another Ford Chevy or Dodge , which girl is the best looking question that I've been asked more times that you can believe when I've got a table setup at trapping conventions .
I hand them what ever snare they have questions about and let them check it out for themselves .

I go with 7x7 5/64 , I've never got into the 1x stuff at all.
I feel it's to stiff, but just my opinion.

I agree with you Chad , chances are if you do catch a fox in a 1x19 snare it'll be where you set it for a bobcat or coyote and a fox beat them to the snare and tried to jump through the snare loop and it gets hip caught .
At least if the snare is 7x7 cable you have a bit better chance at a neck catch because the slight difference in the snare loop believe it or not in that same situation of setting for a variety of target animals meaning coyote , bobcat or fox if the habitat holds all three .

Take it you're not loading your snares.

Yes, I use and recommend 1/16-inch 7x7 Korean cable for Fox & Bobcat's. Also, if you have the right combination of snare lock, kill spring and cable length. Coyotes can be taken with this cable.

When targeting Coyotes? I prefer 5/64 7x7 cable set up as a dispatch snare. Yes, plenty of Fox & Bobcat's can be caught with the 5/64 7x7 cable. I like snares!!!!

SniperBBB you are correct I don't load my snares as I've said many times on here as well as at many trappers conversations Keith Gregerson and I both load snares by putting them in the back of the outfit to go out to set them . I've showed people that a good support system holding the snare and a quality snare is all you need it's a time saver .

If folks want to load them that fine do whatever it is that you need to feel confident to catch you're target animal .