Oh the shin-etsu stuff isn't bad it's just a PITA to apply, and that coolermaster compound thins it out so it spreads better.
You can use any thermal compound on any CPU with the caveat that the conductive types should be applied very carefully to CPUs with exposed bridges etc.
Now I'm not too familiar with what existing thermal interface you might find on a slot 1 P3, but here's the basic principle.
1) remove existing heatsink. This might be as simple as just unclipping it, however some thermal pads stick the heatsink to the CPU pretty good. There's two ways to try getting it off if this is the case, i) get it warm, ii) get it cold. The first can be as simple as letting the CPU run for a while to get warmed up, then take it off while it's still warm. The second is best for pads that intentionally bond to the CPU, you seal the CPU and heatsink in a baggie and put it in the freezer for a while, half an hour or so, and the pad will become brittle. You may need to use a screwdriver to help pry the heatsink and CPU apart. Be careful you don't gouge anything important.
2) Removing old thermal interface. Now you have to wipe off the goop that was on the CPU and heatsink beforehand. If it's a thermal pad, you may need to use acetone or nail polish remover to dissolve it off, do not soak the CPU in this, just wet a rag well with it and rub. Then follow with rubbing alcohol (70% or better) or isopropyl alcohol, or contact cleaner. With paste type thermal interfaces, just rubbing alcohol will do.
3) Checking interface flatness. Now we need to check that the heatsink and CPU we are mating together again are making good physical contact. Get a steel ruler and place it from corner to corner and side to side across the heatsink and also the CPU if it has a heatspreader. Look to see if you can see light under the straightedge at any point. If there is noticable distortion of the heatsink then you will probably want to lap it. Secondly check for smoothness of finish on the heatsink. If there are machining ridges that you can feel with your fingernail then you'll want to snooth them out. Thermal compound is only really a much better conductor of heat than air, metal is better, so you want to get the metal parts as close to each other as possible.
4) Lapping. If your heatsink was unacceptably warped or rough you will want to flatten it. That's what lapping is, flattening, the object of the exercise is flat, not shiny. If your heatsink is very warped or very rough, you'll want to start with a rough grit paper. The higher the number of the paper the finer the grit. Use "wet and dry" paper this is obtainable in the rougher grades from hardware stores, but often one needs to go to an automotive store that sells paints etc, to get the finer grades. If your heatsink is very rough or very warped you might want to start with 180 grit to mow it down quick, for a medium warp or roughness 240 is good. Most people today will start with 400 though because it's rare for more modern heatsinks to arrive that much out of shape. So having decided what grit you are starting with, get a piece of glass at least 4 or 5mm thick, and find a flat worksurface. Modern float glass is one of the flattest surfaces you will easily find. Now tape the paper down to the glass making sure you don't trap any particles underneath, and put it down on your work surface. Now grab the heatsink firmly and use even pressure to rub it in a straight line across the paper, trying to keep it as flat as possible, and not letting the front edge either catch or rise at the end of the stroke. Every few strokes turn it round 1/4 turn. If you're lapping out a warp keep going until it is flat by your straightedge on the first grit. If lapping for roughness, it is a good idea to use a marker pen to make a corner to corner cross on the bottom of the heatsink, so you can check that you are removing metal evenly. When the paper clogs, rinse it under the tap. Some people advocate lapping with the paper continuously wet, I find this too messy. Keep going until the only marks are the size of the grains in the paper. Now move up to the next higher grit. I lap on 240 400 and 600. Some people will tell you you NEED to go to 1200 grit, but I just generally nod and smile at them and make sure to talk to them in a calm voice
When you are done, rinse the heatsink thoroughly under the tap to make sure all traces of grit and metal are gone (Taking the fan off before you do this is recommended!
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4) Now you have your freshly prepared heatsink we can apply the thermal compound. I use the following methods. Firstly I get a cotton rag and use the thermal compound as a polish kind of, I put a little on the sink in the contact area (which might be the whole bottom of the sink or just an area in the middle where it contacts the die directly) and polish it in to the sink real good, this will often make it shiny, or it might make it blackish fromt he metal oxides. Now I wipe this off, then I use one of the following methods. For thicker compounds I use a single edge razor blade to spread a thin film on both the heatsink and CPU, as thin as possible. The razor blade is stiff enough to apply the pressure necessary to spread a thicker compound thinly enough. You need to get a paper thin coating on, thinner if possible. A grain of rice sized dollop should be quite enough for this. If the compound is thinner, I use a baggie over my finger and spread it on the CPU and heatsink with my finger.
5) Now it's time to remount the heatsink. This often requires care that you do not scrape your thermal compound layer. Before I put the clip down I usually wriggle the heatsink down a bit, to try and ease out as much "spare" thermal paste as possible to get the metals closer, and then I clamp it down.
Heh, sorry if I started too simple for you, hope you got out of that what you needed,
regards,
Road Warrior
