Hi, 1991 Silverado owner here - need a little help

[HotWheelsBurban]

I am migrating from some other wheels to the ones in your picture (12325550). I am trying to figure out the lug nuts and caps. I currently have these lug nuts (9595174) and these caps (15646284). My lug nuts are so old and worn, I cannot screw the cap onto them and am worried the caps will just fall off. Also, not sure these are the right caps for those lug nuts. I think the combination goes like this:

Lug nut (m14x1.5) - 9595174
Lug nut caps - 15646250 (for 9595174 lug nut)

Lug nut (m14x1.5x30) - 15551469
Lug nut caps - 15646284 (for 15551469 log nut)

I am looking at buying the 15551469 lug nuts but I cannot see how the 15646284 cap would screw onto it and remain secure? Can you shed any light on that? 15551469 lug nut pic attached.

Would you need something like the 2nd pic I posted so the cap can actually screw onto the nut?

The lug nuts in the bag in the first picture, are what is used on the factory alloy wheels that have a cover over the center like the Suburban wheels, aka Stars, 10 spokes, or Saw blades(6 lug, wider cap but mounts the same) and the 7 spoke second Gen Escalade wheels. Some pics: