I'm no doctor so this is ONLY my opinion, but you MIGHT be able to get away with putting off surgery for awhile, but since the discs are flattening the cord, it won't be long before you will HAVE to have the surgery --- so you might as well have it now before it becomes an emergency situation! You certainly don't want any permanent nerve damage either!
I'm glad you're seeing a Neurosurgeon, but please get at LEAST one other opinion besides this one. Two would be best! You never want to jump into surgery without exhausting all other options!
I wish you the very best. Take care & God bless. Hugs, Lee