Under no circumstance is a measurement in pixels guaranteed to match any given inch/cm/etc. measurement.
Pixels per whatever vary by the monitor you are looking at. And more to the point, on the printer you are printing to.
A quick way to realize that is that your printer is almost surely not printing at the resolution of 96 dpi (dots per inch). Maybe it is, but probably not. If it were, say, 300 dpi, that'd be 300 pixels per inch, in terms of the printer's capabilities. That would translate back to whatever on your monitors.
In any case, there is a much better way to do what you want, and a final consideration after that.
Page Layout View and your measurements, up/down AND left/right will all be in the units of measure your system sets. Inches for me, someone else might use centimeters. Then set the two sizes directly in the unit of measure you need, inches in this case.
That's as close as Excel will be able to come to delivering a true 1" x 1" box on the screen and in a printout.
However, in the real world, even if Excel perfectly renders it (and one suspects it might not), the translation to the printer's dot by dot layout may STILL give you something other than a "perfect" 1" x 1".
So in truth, once you get that far, print a sample and measure. Then, still in
Page Layout View, adjust the measurements as needed to print a perfect box. If it were very important to be just right, I'd shift to centimeters so the fineness of your control would be greater. (You can specify to the hundredth and 0.01 cm is a smaller gradation than 0.01 in.)
But no, the chances of a pixel measurement truly matching something like this is pretty low.