I use paint stir sticks. They are perfect for putting in the satanite and spreading it smoothly. Switch to a clean wet one every so often, and stick the previous one in a bucket of water.
They come in 12, 14, 18, and 21" The smaller ones are crazy cheap ... like 1000 for $30 wholesale. The 21" paddles run about 200 for $85. Buying $85 worth of sticks seems a bit wasteful, but you will find many uses for these. Besides shims and wedges, they are also great for making knife templates and working up a knife shape. They are .125" by 1.125" by 21"
The paint stores and Big Box stores have them, too.
Rigidizer is a good thing to use to stiffen the wool before the satanite is installed. It is sprayed or brushed on the wool and when it dries, it makes the wool stiff. A good trick is to fit the wool roll and then slip out of the forge chamber. Spray down with rigidizer, roll up, and put back in the forge. Let it dry for a few days and then install the satanite. I have read of people making their own rigidizer from boiling sugar in water and applying it hot. When it cools and the sugar crystalizes, the wool gets stiff. I haven't tried it, and my concern is that the sugar will burn when the forge lining is cured. Probably not an issue beyond some smoke and burning sugar smell.
Spritz the wool with a little water, and apply the satanite in layers. A thin mix is what you want for the first layer. A bit like runny pancake batter is just right. This will soak into the wool and make a stronger base for the rest. You are just making a base coat, so don't try for much thickness. Consider it a primer coat. Let dry at least overnight. Apply additional coats in 1/8"* layers. These should be a thicker mix about like yogurt/sour cream. It should not be runny at all. Let each coat dry and build up until the satanite is between 1/4" and 3/8" thick. Don't bother trying to get it real smooth, just even. The last coat can be smoothed up with a damp long handled paint brush.
IMPORTANT NOTE - remember to smooth out and clean up the burner port holes for the burner as you install the satanite. The port holes should be smooth and bell shaped to allow the flame to enter without interruption or turbulence. If you are building your forge with installed ends, smooth the satanite around the front and rear doors/ports, too. It is a lot more work to smooth out or reshape these palces once the refractory is cured. A trick to get a good seal between the lining sides and a swinging door is to put a layer of saran wrap on the door and close it while the satanite dries. This will give a very snug seal.
Once the satanite is applied evenly, let it start drying. Let cure in a warm room for several days to a week. A hair dryer will speed this up, but you shouldn't try and rush the cure time. Check for any cracks, patch if needed, and when all is good, fire the forge under low heat to fully cure the refractory. Start by a short low burn just enough to get the inside hot. You want to steam off any retained water in the refractory. Let it cool for five minutes and burn another short run. Do this five or six times. Slowly increase the heat and burn time until the forge is completely dried out. Run the forge on HIGH until the forge is glowing inside. Let cool overnight, and check for cracks. Patch any and fire again to dry the patch.
Once the refractory is cured, apply a thin coat of ITC-100. This will greatly increase the reflectivity of the refractory and make the forge more efficient and run hotter. You only need a 1/6" of the ITC-100. Mix 2 parts ITC-100 with 1 part water and apply as a layer of paint. If it looks a bit too thick, you can thin it a little more. Build up two or three layers, allowing each to dry overnight before the next. Once done, cure as you did the satanite. I find a half-pint does a normal size forge quite well. You can build it up thicker if you have some left over, or seal it up tight and save for patching cracks later on. Cracks are easily patched with just ITC-100.
TIP:
A really good way to make the ends and also make installing the wool and applying the refractory coating easy is to use Insboard for the ends. It is a 1" thick refractory board that can be sawed and shaped with a rasp to fit the ends of your forge. A band saw or saber saw will cut it easily. It is ready to go as a good refractory, and doesn't need any satanite on it. Fit your wool into the forge shell, leaving about 1.25" on each end ( cut the wool 14" long if you have a 16" shell). This will allow room for the ends. Test fit the wool and ends to make sure all fit right.When each coat of satanite is installed, place a piece of saran wrap over the ends and slip them into place. This will assure that the wool and satanite make a perfect seat on the ends. Remove and peal off the plastic wrap for each subsequent coat. You can do the curing of the satanite with the ends off the forge if your burner swirls good. Apply the ITC-100 the same way, placing a layer of plastic wrap over the insboard ends. When ready for the last coat of ITC-100, apply a good layer to the inside of the ends, apply the final layer inside the forge, and use some ITC-100 as mortar around the rim to seat the ends in place ( no plastic wrap). This will make the ends a perfect seal with the inside lining. Screw in about six stainless machine screws close to the edge around the rim to hold the ends from moving due to expansion. If you like metal end plates, just add them over the ends and tack weld in place ( don't use the screws if adding metal end plates). You can order the round metal plates in any gauge you want from places like online metals. Give them the exact inside diameter of your forge shell (usually pipe), and they will cut the circles to fit. They are really cheap - about $10 each. If you want, they will even cut the port too. A 3"X3" port is good for most basic forges. Make sure you have the port placed in the right place to allow for the thickness of the refractory and wool.
Once the shell and ends are done, fired, secured .... there is the matter of a flat floor coming up to the ports. This is best done with Bubble alumina or Mizzou castable refractory. Both work well, with the bubble alumina being more robust and flux resistant. Mix the bubble alumina with water to a thick concrete like mix and spoon/pour it into the ports. Spread with a long stir stick , adding more until it reaches the ports. Curve it up the sides an inch or two to make the flame have a smooth transition. This will make a robust flat bottom for your blades to rest on.