How can I get my spoke dimensions without knowing the dimensions of the wheel?

Get one of the spokes out ans measure its length. It is a primitive method, but by far the simplest one. Less accurately, you could try to measure it on the wheel and account for the hidden part in the nipple, but I would not recommend it.

When I absolutely have to do this, I very carefully measure with a ruler, ideally one that's graduated to the end, from the elbow to the spot that goes into the nipple, then add 10mm. I take the measurement in a couple different spots until it's coming out the same, because it's finicky. This way is accurate enough. 10mm errs short, which is what you want to do so you don't run out of threaded length or poke the tube on a single wall rim.