Oh, an adventure...! Shinji doesn't go on any of those like... ever, but it's not like they could get more lost in this situation, right? And with Kai still sounding as confident as he does, there doesn't seem to be a huge reason to be panicking, either.

"I hope it doesn't take too long..." even if it will, probably, take a while at the very least. But, he'll let Kai take the reigns on this adventure, surely he's got more experience with that than Shinji does.