When Jonny’s guitar sounds much clearer on a tv performance than it does in a massive stadium, or on a record, it has very little to do with his guitar setup.

Though blurry, this screenshot from Radiohead’s Jools Holland performance of High and Dry shows Jonny using both a blackface-reissue Fender Twin Reverb and a Fender Eighty-Five (youtube).
But first, to clear one thing up: Jonny has basically never used his Shredmaster with a Fender tube amp for distortion. For approximately the first year after Radiohead were signed, the Shredmaster was his main pedal and the Eighty-Five as his main amp. Even when Jonny did start using tube amps in 1993 (such as a Fender Twin Reverb and Mesa Boogie combo), it was only for clean playing. The Shredmaster continued to be used exclusively with the Eighty-Five.

A photo of Jim Warren at the FOH mixing desk during soundcheck before one of Radiohead’s October 2016 performances in Mexico city (avidblogs).
Usually, when you hear Radiohead, it’s either on a studio recording or in a music venue. Even when reverb isn’t used as an “effect” on recordings, there’s basically always reverb added during the mixing stage to make the instruments sound more natural and blend well together. In contrast, Jim Warren (the band’s FOH engineer since the early-90s) rarely adds heavy reverb to the mix at live performances. Since Radiohead basically always play in large venues with a lot of natural reverberation, the venue itself adds all of the natural blending that the band needs (this is a big part of why direct soundboard recordings of Radiohead’s shows sound significantly more dry than album recordings). Jonny’s amps are close-mic’d for both recording and live performance, and in both cases his guitar would sound extremely dry if you just heard the sound picked up by the microphone on its own. But in both cases reverb is being added later to make his guitar sound more natural, which is why many people (citation needed) think Jonny uses reverb effects live more than he actually does.
When Radiohead perform for a television program, they generally play with the same setup that they use for live performances, but they don’t have the natural reverberation of a large venue to smooth out their sound. Just like on studio recordings, this means they need to add reverb. But whose job is it to add that reverb? In recent years, the band have been lucky enough to have the power to bring their own producers or mix engineers with them for televised performances if they want to. But back in the mid-90s, you can be sure that the producers of Jools Holland (and any other shows the band performed on) had total control over how the band were mixed for broadcast.

Jonny uses reverb infrequently-enough in live performance that it was one of the few pedals he didn’t bring along for Radiohead’s 2010 Haiti Benefit show. The odd rectangle of velcro near the center of the pedalboard is where Jonny normally keeps his reverb pedal…
Perhaps in order to make the songs sound a little clearer through television speakers, the mix engineer for Jools Holland probably just added less reverb and mixed Jonny’s guitar louder than John Leckie did on the studio recording. Or perhaps the mix engineer didn’t know the band very well, and mixed the ”lead guitar” much louder than the other two. The mix of The Bends is much less of a “wall of sound” than on the album version, but that means you’d be able to hear Thom and Jonny clearly through bad-quality television speakers. Also, note that the bass is much quieter than on the studio recording (not just the bass guitar, but the bass frequencies for the whole band). That seems to be a common mixing technique for television. Official recordings of live performances from throughout the 90s capture the “wall of sound” a lot better than the Jools Holland televised recording. A lot of the gear at the Glastonbury 1997 performance is different from the Astoria 1994 performance, but the two still sound closer to each other than to the Jools Holland recording.
So when Jonny’s guitar sounds much clearer on a tv performance than it does in a massive stadium, or on a record, it has very little to do with his setup. He may be playing the same song with the same gear, but it’s the engineers who ultimately determine how he sounds and what you hear. This is also a big part of why why Jonny’s TelePlus->Shredmaster->EightyFive setup sounds different on The Bends (produced by John Leckie) compared to OK Computer (produced by Nigel Godrich).

A screenshot of Jonny “bowing” the low-E string of his Telecaster Plus with a coin during the Jools Holland performance of High and Dry (youtube).