I presume you mean a general anaesthetic (put to sleep), that will depend upon the operation that you are going to have, and also on the opinion of the anaesthetist.
"Straight forward operation" should pose noproblems for you as you have another 3days to recover from the cold.
I had an op last year and had a really nasty cold and chest infection on the day, although I felt ok in myself.
So as Sqad has said it's really up to the anaesthetist. Mine checked me over on the morning and gave me the go ahead for my op, so fingers crossed you should be ok!