I don't know that you would have to delete them. I assume there's a random number generator that decides which puzzle to use. Find that in a debugger and change it to always return the # of the hacked puzzle and you should be good to go.
Edit:
It's definitely possible to hack the puzzles. They're stored in regular ASCII, for the most part. The last character in a line has 80h added to it, the last two characters of a puzzle have 80h added to them. I haven't did much more experimentation than that, but I may look at it some more since I have an idea regarding how to use a Wheel of Fortune hack as an educational tool for ROM hacking.
Edit 2:
You can also shorten/lengthen puzzles. I tried cutting off the puzzle I was on early by using the double +80h and it worked fine. Tried lengthening it by moving the double +80h into the next puzzle, that also worked. Not sure how it affects the next puzzle in the cue, though, as I haven't tried figuring out how to trigger a specific puzzle yet. (There appears to be a pointer table directly above the puzzle text, so I suppose I'll look there.)
Incidentally, if you make a save state when the game first says ROUND 1 (white text, on a gray block), you can hack the puzzle and then load the hacked puzzle via that save state.
Edit 3:
That WAS a pointer block above the puzzles. It would be EXTREMELY easy to pull off the hack that IceSageX wants to do. All you have to do is hack a puzzle of your choice and then convert all of the pointers to the value of that puzzle. The only thing I need to figure out now is how the clue (Person, Place, etc.) is determined. The puzzles are grouped by category (for instance, all of the PLACES are listed first, just need to see where it's determined what the label is for a particular group in case the size needs to be expanded for a particular category. (I suppose I should mention that the pointers are in standard NES format. Flip the order of the last two bytes of the location, subtract 10h from the first value and 80h for the second.)
Edit 4: Attached to this post, you will find a zip file containing a proof of concept hack that meets the criteria set forth by the original poster.