The squeak is more likely caused by the interaction of your socks with the linings of your shoes..... I have shoes that squeak like that when I wear cotton/synthetic blend socks. It seems the higher the level of synthetic in the fabric, the more the socks (when combined with some inevitable perspiration) grab the linings and squeak. When I wear the same shoes with merino wool blend socks that breathe and wick moisture away better, no squeak at all, all day long.
Yeah, that fits the pattern too - quiet in the morning and the squeak starts sometime around mid-afternoon. Oddly enough, it's loudest on one shoe, and the other does it a little or not at all, which makes me wonder about the fit contributing.