He worked at a feed store where money changes hand on a regular basis, so it would have been seen as a legitimate request from someone who wants to help out. Hank wasn't a suspect in any way, else they wouldn't have told him about the serial number list in the first place, and it would have made sense for them to give every store and bank in the area a copy of the serial number list anyway.
shareAnd as stupid as the Sheriff was he wouldn't have caught on at all (after the plane was found minus the money)
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The stupid Sheriff was dead at that point
As for Hank asking for the serial numbers, I agree that would've been a good idea for the reasons the OP states
But Hank was, at that point, in no condition to come up with any more plans. I got the feeling he was actually looking for an excuse to be rid of the money, after all it had already cost him.
Besides which, I think he may well have been a suspect. Other posters on this board have pointed out that the FBI agent was himself exhibiting "tells" of a liar while telling Hank about the serial numbers. Maybe he didn't have them. Or maybe he did, and he'd give Hank a fake list, or just half of the list.
Bottom line, Hank could never be 100% certain he was out of the woods, so to speak.