Me, I'd loosen the bottom one, undo the top one.
There is usually enough play in the pipes to be able to pull the TRV out of the way while you whip the blanking plug on.
Or there has been in what little I have done (I'm no plumber) and it all depends upon what yours is like.
The radiator for me has always still been left stuck to the wall as is.
Then once the blanking plug is on (to stop more water pouring out) you can remove the TRV fully.
Have the new one ready to refit quickly, I usually have PTFE tape wound on the threads ready.
An extra pair of hands is always helpful, for wiping your brow, supporting the rad, pulling pipes, bringing brews & passing that spanner that you cant find because you put it behind you Oh and running for more rags & emptying water away.
Whats the worse that can happen, it flood your nice wooden floor & ruin it

Put plastic sheeting down, the edge folded up the wall 12"
with a slit in it so it can go around the copper pipe where you can tape the edges together to seal it.
Then put an old cloth sheet down on top.
That way your doing your best to protect the floor just in case.