Let me follow up your reply with a newbie question. Are left and right side spoke different? The bike is an older low spec Nishiki mountain bike with a conventional cassette.
Is there any way to measure without taking additional spoke off the wheel?
A rear wheel is "dished", such that the spokes on the drive (right) side are shorter than the spokes on the non-drive side.
You could "guesstimate" the spoke length, knowing the measurement is from the bend in the spoke to the end to the threads. You can measure from the bend in the spokes to the near-end of the nipple, then add (guess) the amount of spoke in the nipple.
And of course you should match the diameter of the new spoke to the old - I'm guessing it is 14 gauge.