Most 486 CPU coolers did not require tabs in the socket, they just clip on directly to the processor or use a frame between the CPU and the socket. Other processors, such as Overdrives came with a glued-on heatsink.

The socket 3 tabs were only used for those heatsinks that were attached using a Z-shaped metal clip.

Heatsinks for 486-class processors simply had clips that hooked around the edge of the processor itself. That's how it is in my 486DX4-100 system.This was sufficient at the time because the necessary heatsink and fan was very small and lightweight compared to later processors.

As for how the heatsink and fan is mounted to a POD, I'll have to yield that question to someone else as I have no experience with them.

Just google 486 cooler, and you will see a lot of different types. Most of them are the one that has 4 clips.
These two types, are the ones that you can still find on eBay.

Back in the 90's. Most coolers that I saw, was the type with a kind of frame that were slided on to the CPU
from one of the sides, and with a hole were the heatsink with the entire heatsink with the fan, was
screwed into. Making a tight fit. Yes... The entire heatsink, was a kind of big screw in the bottom.
These days, I can not even find one of those. Today the most common is the one with the four small clips.

I happen to have two of each, but they are all for ceramic pentiums. I couldn't find the clip base for the two screw heatsinks. I took them off because they won't fit on the later cpus with gold humps.

^
I actually have the blue screw-type passive cooler, has MICRON printed on mine. Came with an Intel Pentium 200MHz non-MMX CPU. Probably still in a drawer somewhere. But yeah, the one I have only fits the ceramic Pentium (without gold tops) and the non-ceramic 200MHz / 233MHz CPUs if you use the cooler's clip base.

You need a clip on cooler or one that uses an thermal adhesive pad which was common from the DX2 66 ect onward. I wouldn't use anything that is not reversible as far as using adhesives are concerned.