Deo,

Sorry but I can't understand your problem. You have a stub coming out of
the wall. Copper? PVC? The stub attaches to a threaded fitting and/or a
valve. The cut-off valve attaches to a pipe or hose. Is this pipe or hose
screwed into the valve (compression fittings)or soldered? Your pipe or hose
is screwed into the flush valve.
Basically you want to put a T-piece between the cut-off valve and the
flush valve. If you have a hose then buy a t-piece and another hose. Put the
T-piece between the 2 hoses and attach a hose to each valve fitting. If you
have a pipe cut a space for the T-piece on the pipe and solder or use
compression fittings to put on the T-piece.
You lost me with your fear of shutting off the water. You will need to
shut off the water at the toilet's cut-off valve to do this work. If you do
not do the work correctly it may leak. Take your time and do it correctly.

Dave M.