I've seen people find it strange to have a different skin in the inventory visual screen

and I believe that the simplest way to solve this is by not having any skin there, to do this easily you can use this command in Minecraft:
/effect give @p minecraft:invisibility infinite 0 true

and take a screenshot of your open inventory, then no skin will appear
example:

then you replace the original GUI inventory image

and another thing, when you press ESC and go to Options, Advancements etc, it shows a chest GUI, would be better just show the ESC gui instead