In the US, it makes a big difference as to whether you are labeling your product as "allergen free" or are determining whether you have cross-contact. It is not clear what you are testing with your qualitative test. Is it a swab test or a food sample?
If you are making an "allergen free" claim, a test like this can be used as part of your justification, but you should be sure that you also have an excellent allergen control system in place. The FDA is very strict about "free from" labels. Testing alone may not be sufficient if there are other reasons to think that allergen protein may be present in a food.
You are using a <LOD result from an equipment swab to verify cleaning if you have data to show that the swab is actually performing at this level in your hands with your foods. A thorough visual inspection for residues can be important. Similarly, a quick test such as an LFD using a food extract can be used to verify control if you have data to justify the assessment of performance.
In any testing case, be sure that you are taking enough samples. A single swab or a single food sample do not characterize all the equipment or all the food (unless the food is a well stirred liquid, and even then it is worth doing a replicate).