Just get a used ProCo Rat (standard version) and focus in your playing. Jonny didn't use one, but there's a reason so many people think he did: with the filter knob set right, the Rat has a similarly focused tone to the Shredmaster in the mids and highs.
The Shredmaster and Rat both use opamp hard-clipping followed by diode soft-clipping, so it's not a surprise they're similar (however, the Shredmaster has two stages of opamp clipping). The Rat lacks the post-clipping bass boost of the Shredmaster, but you can compensate for that with amp settings. Obviously, the Rat is less versatile than the Shredmaster, since it can't create scooped tones. But it does a good job of Jonny's favorite Shredmaster setting: contour knob at minimum for full mids and no scoop.
A bonus of getting a cheap, used Rat is you can quite easily modify it with a "clipping" switch, which gives access to Turbo Rat tones (the Turbo was Thom's favorite drive in the 90s, and that's probably the reason people used to think Jonny used a regular Rat). You can also get a Turbo Rat and add a switch for regular Rat tones, but the Turbo is usually pricier. Or, if you're particularly interested in soldering, you can build a mini Rat clone for about the price of a used regular Rat.
A shot of Thom about to stomp on his ProCo Turbo Rat during 2+2=5on the Jonathan Ross show on November 7, 2003 (youtube).
Another Radiohead-related option is a Boss OD3, one of Jonny's favorite overdrives since ~2006. The OD3 has a distinctive tone of its own, but with the tone set right it has a bit of Marshall flavor too. And, like the Shredmaster, it has a post-clipping bass boost for a fuller sound. I also think it's a nice starter pedal, since it's more dynamic and "amp-like" than the Shredmaster and Rat (that's due to the OD3's discrete-opamp soft-clipping circuitry). It's quite usable from low to mid to high gain, so it could easily be your only drive pedal.
For settings, check the Fender Eighty-Five entry on Jonny's amplifiers page. But remember: even replicating his settings exactly will still sound different from studio recordings, because you're missing the signal chain after the amp's speaker (mic, EQ, compression, gates, etc). So (as always) it's better to use your ears and tweak the settings to find those sounds. We discuss this in more detail in this post.
A photo of Jonny performing with Radiohead in Kansas City in 2012 (Jason Squires). You can see his Shredmaster and his OD3 on the board on the left.