Do you have a Dremel, or other rotary tool?
I guess if I were doing it, I'd start by snipping off the cable (or snip it as short as you want it, if you're aiming to keep some of the cable).
I'd consider checking for any screws or obvious methods for opening it. If there is nothing, that's fine - skip that. If it can be opened, maybe try opening it and see about removing any electronics you can without screwing up it's ability to keep the exterior appearance intact. (Like, if removing innards, makes it impossible for the lens part to sit in place, then maybe just leave things as they are).
Next, I'd take an existing Rainbow High Doll and measure the size of the existing head hole. Then I'd draw a circle on the webcam in that size where I want the hole to go. (Probably aim for drawing it on with something you can remove, or maybe try drawing on it with a pencil.
Using a dremel and some sort of drill-type bit, start by putting a hole in the center of the hole you've drawn.
I recommend getting some bits like this - Carving Bits
Go slow, and aim for keeping your hole -smaller- than the circle you drew.
I have no idea what to expect from the interior of this thing, so there's going to be some improvisation depending on what you encounter.
Try doing some tests as you go, seeing if you can get the neck to fit in the hole at various points to see how things might be working.
Whether or not you'll need to put something on the inside of the webcam is gonna depend on your tests.
When the hole is a size that works, you'll want to sand the edges with sand paper. You'll probably need to take an xacto knife and go along the inside to remove any plastic burrs.
Thanks. I used a dremel with the bits below to get them close then hand files to get them flat then 1500 and 2000 grit sandpaper.
Rokrou Carbide Double Cut for... https://www.amazon.com/dp/B097CY5NK5?ref=ppx_pop_mob_ap_share