The "squeek" usually results from moisture from the foot adhering to the instep of the shoe.
Powder is the fastest way to determine whether or not that is the reason for the problem.
I know of nothing else but wearing a shoe liner, but except for walking in a library or church, I'm more bothered by lumpy shoe liners than by squeaks, and of course shoe liners are silly looking with sandals.
There ARE some shoe liners that have a fabric covering, but they work about the same as the sock type.
Is putting a bit of powder into the shoe each time it's worn problematic?