The line of questioning is almost entirely useless in the first place, and the way that they will interpret the evidence is likely the opposite of the way it should be interpreted.
Ordinary people know basically nothing about explosives, or what everyday compounds might be explosives. At best they might say "Oh, I did some gardening, so I handled some fertilizer", or "I was at a shooting range yesterday". They might remember a chemical they had read off the label of something they used recently, if it's common enough, so if you told them what you found, they could tell you where they saw it.
Terrorists, on the other hand, are likely to know all about common chemicals that can be used in explosives. If you tell them what you found, you aren't giving them any new information, and they can just tell you it came from whatever they got it from (and claim they were using it innocently).
So giving a satisfactory answer should actually be evidence of the person being a terrorist. Of course, if a TSA agent were smart enough to realize that, a smart terrorist might pick up on that, and say "I don't know, I used some bug spray this morning?"
Most terrorists don't actually seem to be smart, but in the case that you were evaluating the evidence correctly, you'd have to downgrade its strength on that basis (even more so once you factor in the non-terrorist chemistry geeks, who are probably orders of magnitude more common than terrorists, and less likely to consider that you might take a plausible answer as evidence against them).
In short "what have you handled recently that might have lead to you having explosive residue on you?" is a pointless question, whether you tell them what you found or not.
As a side note, it's overly simplistic to say that "giving hints" is invalid in general, because the definition of "giving hints" is vague. Should they just ask "Why did our screen flash red?" instead of telling you it was the explosive detector? Should they be even more vague and ask "Why are we interrogating you?" Getting useful information from someone requires that you communicate specifically. So if the line of inquiry were useful at all (and if it is even meaningful to reason about such a hypothetical), it would be more useful to ask about the specific substance.
Ordinary people know basically nothing about explosives, or what everyday compounds might be explosives. At best they might say "Oh, I did some gardening, so I handled some fertilizer", or "I was at a shooting range yesterday". They might remember a chemical they had read off the label of something they used recently, if it's common enough, so if you told them what you found, they could tell you where they saw it.
Terrorists, on the other hand, are likely to know all about common chemicals that can be used in explosives. If you tell them what you found, you aren't giving them any new information, and they can just tell you it came from whatever they got it from (and claim they were using it innocently).
So giving a satisfactory answer should actually be evidence of the person being a terrorist. Of course, if a TSA agent were smart enough to realize that, a smart terrorist might pick up on that, and say "I don't know, I used some bug spray this morning?"
Most terrorists don't actually seem to be smart, but in the case that you were evaluating the evidence correctly, you'd have to downgrade its strength on that basis (even more so once you factor in the non-terrorist chemistry geeks, who are probably orders of magnitude more common than terrorists, and less likely to consider that you might take a plausible answer as evidence against them).
In short "what have you handled recently that might have lead to you having explosive residue on you?" is a pointless question, whether you tell them what you found or not.
As a side note, it's overly simplistic to say that "giving hints" is invalid in general, because the definition of "giving hints" is vague. Should they just ask "Why did our screen flash red?" instead of telling you it was the explosive detector? Should they be even more vague and ask "Why are we interrogating you?" Getting useful information from someone requires that you communicate specifically. So if the line of inquiry were useful at all (and if it is even meaningful to reason about such a hypothetical), it would be more useful to ask about the specific substance.