Modern figure skating au where Shenkov is an ice dancer is so in character imo. why? here you go:
In ice dance, unlike in freestyle, being tall/broad isn't a deficit and is actually a physical advantage (height especially) because it makes it easier to lead the female partner, as well as gives you more leverage for elements like lifts. Shenkov is described as being "tall and powerful... but with the grace of somebody who considered failure to keep fit a betrayal of the Soviet duty of labour." He's tall without being overly muscular/bulky, and (at least in Valery's immediate opinion) quite naturally graceful. I don't think it's a stretch to assume he has long limbs, so in other words he's the exact 'perfect' physique for a male ice dancer to create those strong, elegant, elongated, (romantic!) lines.
Male ice dance partners are also supposed to be sort of in the background. They're not supposed to be cardboard cutouts, but functionally (traditionally) their job is to support the female partner and let her be the 'star.' Usually when people imagine a 'male figure skater,' I think they conjure a pretty flamboyant image, but that's a lot less of a requirement in ice dance so I feel it fits Shenkov's very reserved personality (don't get me wrong-- ice dancers have lots of flamboyance and flair, and there's absolutely nothing wrong with being really showy! It's just more typical for the male partner to be much less so than the female so they don't clash, and it all depends on the tone of the program).
If you're unfamiliar with figure skating, ice dance may appear to be boring/simple because it's extremely technical in the fine details, which can just be hard to notice if you don't really know what you're looking at. Frustratingly, I can't find the quote right now, but somewhere Valery remarks about how Shenkov is constantly modulating the way his emotions are showing on his face so that he can appear more blank and intimidating. From Shenkov's POV chapters and Valery's narration, we see how aware Shenkov is of his physicality-- he uses it purposely to intimidate people with his size and strength, but he is also extremely self-conscious that that's the impression people are constantly getting from him. Something about how Shenkov is detail-oriented, very tightly in control of his movements and his emotions and his face reminds me of the intense precision required in ice dance, as well as the acting that skater's often do tell a story along with the music.
And lastly, ice dance is the 'girliest' of all the disciplines a man can participate in, IF you decide that all the jumps and dramatic throws that are present in freestyle and pairs are the more 'masculine' elements (I personally believe this assignment is bullshit, but it's present in the perception of figure skating as far as I'm aware). I think it's really ironic that someone as physically dominating as Shenkov would excel the most at the more 'delicate' of the disciplines, but he would!