Will GM 200r4 work with factory floor shift location?

I see no reason why you couldn't use a cable instead of mechanical linkage. Yes it would be easier and faster and require less fabrication. The only small problem (very small) is getting/locating the hole in the trans lever to catch all the detents. Most of the aftermarket shifters have a hole or two where you can attach a cable but you will probably have to manufacture a small bracket to secure the threaded part of the cable. I'm sure you've seen them in Jegs or Summit (see pic). There's a threaded end with two jam nuts. You make a small bracket put a hole in it the size of the threaded part of the cable that find a spot to mount the bracket under the console. You just have to make sure you mount the bracket at the correct distance from the shifter levers so that you get the full stroke of the cable and the shifter. I had to build a small bracket for the '35 Chevy I built. It's pretty simple. Hope this helps.
Do your best to line up the cable and bracket so that there is the least amount of resistance and the best alignment (It makes the cable slide easier).
Oh wait did you say you wanted to use the stock shifter...if you did then the answer is still yes. I believe they also sell cables with a 90 degree end on it so you can stick it in the hole on the shifter lever or you can use a small clevis (makes it simple)

Treblig