Probably a dumb question, but here goes:

Is there any way to swap out shifters without loosening/removing the shifter cable from the derailleurs?

Yes and No.

I can't visualize a way right off hand. Think of it as an opportunity to install nice new cables. You need to learn to adjust derailleurs, Park Tool is your friend Repair Help Articles | Park Tool

For most shifters, the answer is no.

Easy, cut the cable somewhere along the down tube. Change shifters, then tie the ends back together in a knot.

Well, not the FIRST time, but if you want to do that for some reason on a regular basis, there's quick disconnects

I was surprised at how well those work. I was expecting to have to adjust my derailleurs every time that I disconnected and re-connected the shift cable. I didn't find that to be necessary.