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That is one Hell of a tough question! Here are a couple of possibilities (starting with the one I find most likely):
The F-101 "Voodoo". It's got a unique fuselage design which would lend itself well to the concept of being better aerodynamically from reverse, and it wasn't outfitted with any machine guns or cannon.
The F-4 "Phantom". This one really doesn't fit the bill, but since it didn't originally have any weaponry other than missiles, it meets part of the criteria you specified.
Other than that, I'm stumped!
If you need a new question, try this one:
Who was the first man to break the sound barrier without the use of a vehicle of any kind?
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