Fate Zero
I just imagine reincarnated detective Kishiar unintentionally summoning Yudrein as Assassin in Fate Zero when he chases down the serial killer and comes across the magic circle he made. Kishiar wonders why Yudrein is so familiar. Yudrein tells him about the Holy Grail War and asks him what his wish is.
Kishiar's wish is just to know who Yudrein is, but instead he didn't have one before (was bored while going through life as a genius in a peaceful world with nothing that interested him), but now that he does, it's a secret. Is Yudrein fine with that?
Yudrein is.
Yudrein helps Kishiar track serial killer and Caster (Yudrein replaces the Assassin because I find serial killer and Caster duo so much more interesting and Kirei gets Gilgamesh later anyways) (though Yudrein could totally be a Caster) while exploring the incidents happening across the town (the fight between Saber and Lancer, Rider stealing maps from places and destroying property in the process, etc).
Would love to see Yudrein participate in the discussion about Kings between Saber, Rider, and Archer. Gil would totally call Yudrein out as a dog, asking why Rider invited him, but then come to respect Yudrein because Yudrein's just a person worthy of it. Debating on if Gil would like Yudrein too because Yudrein is kinda Gil's type (tragic hero with despair face - or in Yudrein's case, sad kitty lol).
Anyways, Yudrein's opinion on what a King should be like would be based on Kishiar and Katchian (his Commander and the Emperor he served).
As for the War, I imagine Yudrein would be able to defeat Caster for Kishiar and I'm too biased to comment on the fights with others lol. But for Happy Ending, Yudrein becomes human along with Gil when the Holy Grail breaks. For Bad Ending, Yudrein gets eliminated by Gil's Noble Phantasm.
(Sorry, Rider, but I think Yudrein could beat you. And Saber.)