My thoughts are you (or the Pro) needs to treat the pseudo-new floor as a refinishing job. I don't know what's necessary to refinish your cork floor. I do know a Screen Sander could be used. However, you'll go through a lot of screens. The belt sander is messier but a Pro should know how to use it to avoid 'gouging' the wood.
RE: Water vs. Poly - It depends. There are pros and cons of both. I recommend a poly product for flooring. It does take longer to dry and it is odor-ful, but it doesn't dry to a milky color and will last longer.
My best to ya and hope this helps.
Jay J -Moderator
PS: God Bless America!