There is, actually, a means to assign different camos to each of your weapon palettes via creative use of shortcut commands. But keep in mind that this is a bandaid fix at best, and is a bit of a hassle of setup/manage, + isn't really viable for use by gamepad users.
First, let's start by going over the relevant shortcuts.
/mpal# --> Used to swap to the relevant weapon palette slot. For this to work, you would want to assign shortcut command slots 1-6 with /mpal1 - /mpal6, respectively.
/cmf *CAMONAME --> Equips the desired weapon camo, should it be present in your inventory. Note that if the camo's name contains spaces, you will need to remove those spaces in order for the command to work. (ie * Ideal Rafale becomes *IdealRafale)
/sr RINGNAME is another shortcut worth bringing up. Like with camos, you will need to remove any spaces from the item's name here. You can use this command alongside the other two I listed, in the same command, to swap weapon, weapon camo, AND the skill ring all at once! Quite nifty, if I might say so myself.
So with all those commands in mind, you can simply set up your shortcuts, then swap your 'change weapon' keybinds to use shortcut commands instead. The shortcut commands will then function as an all-in-one weapon/camo/ring swap, after all.
One final word of advice/warning: If you want to play multiple classes, your shortcut command has 5 'pages' you can swap with the /swp# (1-5) command (or just use the dropdown list in the chat shortcut menu. Either works.) Essentially meaning that you can set up commands for up to 5 different classes on a single character with this route.