May I look at the woman discreetly without her knowing?

Yes, according to the Shafi'i school, and it in fact better protects the woman's feelings if the man ultimately does not go ahead with the proposal.
Jabir bin Abdullah r.a. related that after hearing the Prophet's ﷺ words about looking at a woman one intends to propose to, he hid himself to see the woman he wanted to marry, and then went ahead with the marriage. The conditions: a genuine intention to propose, looking only at what is normally visible (face and palms), not peering into the home or when she is not covering her ʿawrah, not following or harassing her, and not taking photos or videos secretly. If he is not drawn to her, he should stay silent and not tell others. Another option: ask the family to arrange a chaperoned meeting.