Even during the auction, it is pretty simple to change the category, and some other details about the auction. You can do even more if there aren't any bids on it yet.

You can, when you're signed in, got into your auction and press the revise auction button. You can do a lot of things without cancelling your auction, and even more if there are no bids yet. I used to do it all the time because I was always in a hurry posting and made a gazillion typos and was constantly changing the wording and title.

I, too, after over 500 sales on eBay, didn't think of the ease of shill bidding in private auctions. Makes sense, though. I know you can change the category at any time, but if you'll garner some extra bids by canceling this auction and re-listing as an open auction, I'd at least consider it. All it will cost you is the listing fee.