Yes, the SCPH-39003/39004, the 5000x series will work fine if you don't mind losing the i.Link port. You probably don't need it, unless you want to run a UT99 lan party
(it's the only PS2 game I have that supports it, anyway).
About that hyper dusty PS2 - I would touch that! Very fun project to spend some time on, IMO. The warranty seal in the back is still intact. All it needs is some love, clean it up, replace all of the worn down thermal pads and that PS2 would be probably mechanically perfect. I fixed up a 39001 (US model) that a friend of my brother's dropped by our house because he didn't want it anymore. It was in very similar condition, but it had been opened before and had a very old version of the Thunder modchip on it. I removed the modchip even though I have a latest gen Thunder Pro 2 Gold (which is a Brazilian-made, but the most advanced PS2 modchip around). There was no point, installed an HDD kit and FreeMCBoot and it's just as good to use, if not better than my old modchipped 90001 (especially now that its laser died).