I do not think Ilya is any more comfortable with the idea of not appearing masculine than Shane is. He would not be okay with someone assuming that he's the more feminine of the two and he does not act that way.
I'm pretty sure this is just more compensation for the ultra feminized-Shane trope, but as we've all acknowledged, you're not exactly fixing the gender binary by switching which one is "the woman".
The thing is, Ilya doesn't show as much effort in fitting a masculine ideal, because it comes naturally to him. He is naturally the kind of person that fits hockey's very specific stereotype of masculinity. He is loud, brash, aggressive, provocative and openly and overtly sexual. He likes fast cars and red meat and coca cola and probably has done an illegal drug or two at the club.
There's nothing wrong with any of that, by the way. (Well, I mean, the hypothetical drug use would not be legally advisable...)
There's also the fact that RUSSIA has its own ideals of masculinity and, while I wouldn't pretend to be an expert, it seems pretty clear that Ilya does a good job with that too. He takes care of his family. He comes home regularly and makes sure his ailing father is taken care of. He is a provider. And even when he finally kicks Alexei to the curb, he makes sure that his father's burial is handled, gives Alexei his apartment, and sets up a trust for his niece.
We do however see that Ilya has that very traditional masculine trait of hiding his vulnerability and emotions. It takes five episodes, and two equally vulnerable declarations from Shane, before Ilya is remotely willing to open up to him about his family and fear. Svetlana is the one who put everything about Jane together while Ilya's still staying closed mouthed about everything.
It's very much a stretch to me to take that guy and say "oh no, he's fine if people think he's femme". (Especially since the sole basis for this seems to be a very eurotrash-stereotypical leopard print shirt).
For the record, I also do not think Ilya would ever drop Rozanov for Hollander upon marriage. Even leaving aside that "Rozanov" is the basis of his career and branding - married women do sometimes keep maiden names for professional use and married names for personal use - he's NOT a woman. And even if he hates his family (and I don't really he does), it's still IRINA's name. It's HIS name.
I do however think they'd hyphenate. Mostly because Ilya would enjoy being obnoxious about the sheer length of that 16 letter plus hyphen surname. And also, I think he'd find it a turn on to see Shane labeled with HIS name like an ownership stamp. (And Shane gets to enjoy that too!)