It seems like a fight is inevitable but I wonder if he'd at least get the guy's respect for the future if he came clean, lol. He's got a few screws loose so "sorry the truth is I'm a spy, let's fight" might have him be okay after if you can beat him.
I mean surely there's no way he didn't realise Yodaka was a spy immediately. This seems more like he's just fucking with him to see what happens.