Ah "may contains". Hate it. My son has a nut allergy and the amount of stuff which allegedly contains nuts is shocking. That said, I went to a copackers recently who were packing nuts, doing a dry clean then packing pasta on the same line!
Despite all my years in the food industry I never expected that!
I agree with the previous poster, risk assess, risk assess, risk assess. What is the genuine risk of cross contamination between your wheat and non wheat products. Now, and here's the important bit, even if you chose to put a disclaimer on pack, you should still try and minimise the risk of cross contamination as much as you can. Not sure about US legislation but in the UK if you put "may contains" on a product but it actually contains a detectable level which isn't listed as an ingredient, you are still on the wrong side of the law anyway buddy. The disclaimer statements are comforting to manufacturers but most allergenic consumers ignore them.
So now I've taken you out of the cosy world where the warning isn't worth the packaging it's written on, what do you do next? Well you look at various things you can do to control the wheat.
Where is it stored?
Where is it weighed out?
What form is the allergen in (light powders can be a pain for example).
What can you do to control the spread of the allergen? Do you need specific weighing equipment, PPE etc?
Where are the hot spots where contamination is difficult to control? They might be where the allergen is most concentrated and in a form like liquid or powder where spillages could be likely.
Where do you use shared equipment?
Can you plan to do non wheat before wheat containing lines (if you have an end of day clean)?
If you have to do wheat before non wheat, how do you validate your cleaning (e.g. ELISA swabs, ELISA testing of the positive control containing wheat and the first few products of non wheat to prove no cross contamination?)
Can you use rapid swabs post clean if they'd add value to your process? This might be a good idea if you are this wary.
Only after all of that control and working on improving it would I still then say you're doing everything you can to stop cross contamination. Even if you and your bosses aren't brave enough to remove that warning, you are still doing everything you can to protect a vulnerable consumer who is fed up with everything they pick up saying "may contain".