Time for some good old fashioned bullshit.

'Alright Kazuma, calm down...' Kazuma thought, taking a deep breath. 'He clearly hasn't caught on that Aqua is the reason he's here... For once, her inability to act like a competent goddess might be working in my favor... I might be able to misdirect him somehow... Just fish for a bit more information... And weave together some bullshit that can send him elsewhere... Maybe I can get him on a wild goose chase...'

"Is everything alright?" Beldia asked, turning his head to look at Kazuma. "You seem deep in thought."

"Ah, I'm just trying to remember if I saw anything that might fit the bill of what you were talking about," Kazuma half lied easily. He had been doing that, he was just staying mum on the fact that he figured it out. "You said it came to Axel Town right? And then you headed over to investigate?"

"Correct," Beldia moved his head with his hand to simulate a nod.

'Perfect... I just hope that my hunch is right...' Kazuma thought, praying that what Beldia said next would make what he was about to suggest to the Dullahan plausible. "How long did it take you to arrive and set up shop in the castle, and then set up some undead birds to fly over town for you?"

"It took me a few days to arrive, and then another to kill and reanimate enough birds to have a viable search party," Beldia explained. "Why do you ask?"

"I just had a thought... What if what you were looking for was no longer in Axel Town? If it was a person or animal, given what you just told me, it would have had ample time to move on, right? Hell, it may have even been some kind of sacred item that someone picked up and went elsewhere with, I don't know..."

Silence. Aqua was staring at Kazuma, gaping. The rest of his party was rather confused, but going along with it. Beldia was stock still.

"...I am a fool... How could I have missed such an obvious possibility!?" Beldia panicked, sweating heavily. "My quarry, whatever it is, could be halfway across the world in the time I wasted here! I shall have to make preparations to leave as soon as you are on your way back to Axel Town! You have my thanks for your assistance in my investigation!"

"Well then, we shouldn't keep you!" Kazuma said cheerfully, mentally celebrating. 'Sucker!' He looked at his party, and asked, "Has everyone has their fill?"

They were still too stunned that Kazuma had actually pulled persuading Beldia to leave off to answer.

(Hehehe... Yes, Beldia will be spared, for the time being at least. I like him too much to kill him off as quickly as canon did... But I am not above screwing with him just as much, if not more than canon did, and now he's going on a wild goose chase! Once again, Kazuma's deception saves the day!)