Can I just turn off the cold water and allow the cylinder to drain
below the shower level or is that not possible with an unvented
cylinder?

There should be no need to drain the cylinder at all. If you cut off the
cold feed to the tank, then no water will come out of the top, as it needs
to be pushed out by the mains pressure.

Try turning off the kitchen stop cock. The hot taps throughout the house
should immediately stop working. Sure there will be a few dribbles, but as
long as you use a compression joint to connect to the pipework, there
shouldn't be a problem. Compression stop ends are easily obtained, but try
to install very close to the original T, so you don't have a load of
stagnant water sitting around. Better still is to remove the T, but this is
more work.

Christian.