Any regular thermal compound would be fine.
I don't know where this idea keeps coming from / spreading that stuff needs to be repasted every few years (perhaps modern 300+ Watt TDP hardware/chips/GPUs??). This is NOT how any (decent) thermal paste works, though. If the chip isn't running at 70C or more all the time (unlike some modern hardware), any decent thermal past will NOT dry up.... or not that fast. With a cool-running CPU and decent paste, expect 10-15 years -AT LEAST- from your TC.
I also don't know where the notion comes from that thermal paste "needs" to be replaced every time a CPU or GPU is removed - that's also a load of crap. If the thermal paste has not lost its properties - that is, it's not dry and not contaminated with (too much) dust or dirt, it can be scooped up and spread back again to reuse. I've done this to almost every vintage/retro system I have refurbished (save for a few very dusty systems aside, where the TC really did dry up from the high temps from the clogged heatsinks) and have not had any problems with the hardware in 10+ years. Matter of fact, my 3 GHz P4 Precott Dell PC that I use daily is 20 years old exactly. I got it back in 2012 and took out the heatsink for a CPU "upgrade" (going from a 2.8 GHz to a 3 GHz, it that can even be called an upgrade :p ). Since the old paste was OK (not dry or dusty) I scooped it up and re-spread it. Still works fine 13 years later without overheating. And that's a pretty hot Prescott CPU (89W TDP, about 115W peak power at max load.) I do this on GPUs with exposed dies too all the time as well. Max difference I got was around 3C between that and new TC. I suppose if you have a bumpgate GPU that's already running too close or above the "critical" bumpgate temperature (70C), then doing anything to help shave off a few degrees might make slightly more sense (though, IMO, if you're in that boat, you'll be just better of getting a bigger/better cooler.)
So anyways... just use any regular PC thermal compound and don't worry about it.
P3's are so cool (pun intended 😀 ) that you probably won't need to repaste the thing even 20 years from now.
See you back in 2045 here!