I need to change the rear mech inner cable on my Giant Fastroad slr1 (2016). The cables are run internally through the frame, but I need to know if it is a continuous outer sheath or is in sections, does anyone know please?
Specific to your bike? Nope, no idea.
But you can test if its a full housing by push/pulling the housing where it enters the bike and see/feel if it moves at the exit point. This is often visually like a wire disappearing into a wall. By threadding the NEW inner into the OLD outer in place, you can then pull the OLD outer out the back and feed a NEW outer up using the NEW inner as a guide. Its easier to do than describe.
If that doesn't help, release the inner wire down at the mech to give you some slack. Then gently pull the outer away from the frame entrance or exit. You will probably see the inner cable disappear into the frame.
Try and pop any cap or cover loose. If this works easily, then your bike has no guide pipe inside the frame, because you can tape the NEW inner to the OLD inner and guide it through. You'll want to pre-fit the new outers at the front of the bike first, and probably end up having to cut the head off the OLD cable.
The hard thing now is risking whether there's a guide pipe inside the frame.
You might get an idea by feeding the OLD inner into the frame at both ends and listening for a "tink" of the steel wire hitting the frame on the inside. Won't help on carbon bikes. If you DO hear a metal tink then its probably not piped inside. If you DON'T hear a tink, means nothing.
Basically now you have to pull the inner and then push a new one in and hope that it doesn't drop into the frame.
Specific to your bike, I see this image:
Zoom in and there's a loop of black inner cable that drops out just in front of the bottom bracket and loops underneath. Look to be a medium sized square/rectangular plate that may undo.
Please have a close look there and see if the plate comes off easily. Do take some clear photos and post them in your own answer, showing how you found it.
You could try shifting into the largest sprocket, stop turning the pedals, and then shift the shifter down into the smallest sprocket, thus making the gear cable go slack. You might be able to pull the outer cable out of the seat where the cable from the shifter disappears into the frame. If you can do this, and see the inner cable, then the outer cable is not continuous.
However, there might be a separate sheath that the inner cable feeds through inside the frame.