It shouldn't take more than a screwdriver to remove the blade and take it somewhere where they sharpen knives and other tools.
I have the same need here with my old time school office paper cutter & I was thinking that maybe if I called a lawn mower shop because the mower blades sometimes also need sharpened -- maybe they could do the honors !!!
If I had to take a guess at a solution, I 'd say to try cutting aluminum foil. This is what I've heard is recommended to sharpen scissors.
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