Edison?
"Upton, who joined the laboratory force in December 1878, provided the mathematical and theoretical expertise that Edison himself lacked. (Edison later revealed, "At the time I experimented on the incandescent lamp I did not understand Ohm's law.""
"I do not depend on figures at all. I try an experiment and reason out the result, somehow, by methods which I could not explain.")
Of course we need to ask was Edison doing physics or "just" inventing? I would argue siome work was experimental physics. e.g., one of the accidental discoveries made in the Menlo Park laboratory during the development of the incandescent light anticipated the British physicist J.J. Thomson's discovery of the electron 15 years later.
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What about Hubble's assistant Milton Humason?
What about the astronomers who found/find variable stars through inspecting photographs?
What about the citizen science project at Oxford for determining galaxy types? That's definitely experimental, and you can do that (now!) without using any mathematics. Some very strange objects have already been pointed out by observant citizens, so this might become an important project:
http://www.galaxyzoo.org/
OK some of this work is pretty menial, but so's much of the number/algebra crunching :-)