They already tried with Trump, anyway, and that's about the only one that comes to mind that would have caused a worse stir.

Honestly, I think Kirk is actually a worst pick for them then Trump. Even on the right Trump's own attitude can come off as divisive and boorish, it's one of the things that drive a lot of people to him but it's also one of the things that drives people away, I can't tell you how many people I know personally that say "I like a lot of what Trump's doing but I wish he'd just shut up". Kirk was a genuinely nice guy where the only negative things people can say about him are lies, they can disagree with him, sure (hell, I disagreed with him a lot), but he was patient and respectful even when crowds of people were shouting right at him, he gave an open mic to whoever wanted to say something, he constantly told his own side to be quite and let the other side speak, he never advocated violence or hate, even if you think some of the things he said were wrong you couldn't deny that they came from a place of compassion (for example he didn't oppose trans ideology out of hate for trans people but because he wanted them to live better quality lives and believed that the trans lifestyle was hurting them), he was basically the political version of Mr. Rogers. Also take into account that most Trump supporters are probably Kirk supporters as well but that's not going to be true the other way around.