When I line my Forge, I mix satanite and water till it's thin like paint. You can put it on with your hands or with an old paint brush. After you fit your kaowool, coat it good with the mixture. I was considering fitting the kaowool and then dipping it in the mixture and putting it in wet. There's probably dozens of ways to do this. I like using my hand so I can feel all the seams to make sure their covered..... hope this helps
If you're worried about it just use a toothed squeegee/trowel and apply some stove cement ot the walls of the forge as though laying tile. You don't want to get the wool toogummed up because it makes it a worse insulator. Apply the wool to the wall with enough pressure to embed it. I would probably dothis next time, but the first typ I didn't. and it seems to have come out OK.
Also cut the wool so it is a tight fit, and that will hold it in place and improve thermal performance, unless you overdo it.