Should I take delay " a few days" as a polite decline or literal?
Of course it’s impossible to be sure, but if the professor didn’t intend to do anything about your paper, I consider it likely that he would not have answered at all or that he would have answered that he lacks time. The latter would have been the polite decline – there is nothing polite about saying that you will do something without ever intending to do it.

What is uncertain is whether and when the professor actually does as he intended. Many professors are notoriously busy and underestimating when they will find time to do something. Moreover, they may be disorganised and just forget about it. Depending on how urgent and important this paper is to you and whether you delay anything waiting on the professor’s response, I suggest to write a polite and short e-mail stating when you would need the response and that you understand if he would reply that he is not able to respond to your request up to that point.