I would guess the toe box of the shoe is too narrow or too shallow, which could also be the cause of the same problem you have with some of your other shoes.

A neuroma would be driving you crazy pretty much all the time. What you're describing sounds more like a transient compression problem. The weakest link gets smooshed the most, and for you that may be the nerve running out to the 4th toes.

Do you have a pair of running sandals? Or running shoes that lace well down into the forefoot? Maybe try running in them to see if the problem shows up even in a more open toebox (mind you, a sandal doesn't really have a toebox, but you know what I mean.)

Also, pull out the other shoes that cause this problem and compare them to the shoes that don't. Pay close attention to the width and depth of the various toeboxes.

Sometimes it's fun to stand on a piece of paper and trace your bare foot, cut the tracing out, and hold it up to the underside of the shoes that irritate your toes. It can sometimes be an eye-opener, especially if the tracing is wider than the shoe.