Always a bit of a pain isn't it? The quickest answer to this would be: work FAST... I have never tried the green putty myself so i don't really know if its waterbased or solvent based putty. I did try to thin my solvent based putty with some mineral spirit in the past and it kinda works to keep it wet but tends to make my putty grainy.
I always grab a little tamyia tape and stick a few strips to the bench. I then squirt a tiny glob on it and start stirring with a wooden toothpick right away. You always use too much putty so work with small quantities. For instance i tape off the top half of my model and apply the putty. Then i reapply new tape on the bench and get a new small glob after i taped of the undersides and so on; in other words, i work in stages.
Richard