You really have to take the fear of rejectection out of the equation. I’m going with the assumption that the yes or no is for a date, not marriage, so correct me if I’m wrong.
If after doing your research the girl seems like a good candidate/match then definitely say yes, and let the chips fall where they may – or as you consider calling it “play G-d” (not so apt, IMHO). If however you KNOW that this girl is looking for “Moshe Rabeinu” and your son obviously isn’t, you can ask the Shadchan his/her opinion of why he/she thinks it might work. Perhaps this girl is not such a “big shot” after all, otherwise it wouldn’t have been suggested. If the Shadchen backs off after the question then so can you. If not, it would be wise of you to say yes and remember that each suggestion brings you closer to the right one. Most importantly bear in mind (and repeat to your son) that all you need is THE ONE to agree, and thank Hashem for all the rejections as they are actually making the agonizing decision process a whole lot easier for you. Hatzlacha!
And definitely saying yes (despite there being a good chance of getting back a no) if you genuinely feel it’s a good thing does not demonstrate a lack of bitachon. Just the opposite, it shows that you are doing your hishtadlus, yet are leaving the reins in Hashem’s hands.