Like masMalkar said, using perfumes is the easiest option (calm is the most relevant option since it directly lowers "contact" stress, but you may also want to put on stasis, which slows the gradual stress buildup).
Aside from that, stripping an applicant incurs stress, both from the initial strip and from the accelerated idle stress buildup afterwards. Touching a naked body part also incurs more stress (and pleasure, but that's irreverent if your focus is actual border-guarding) than it would have on their fully-clothed counterpart.
Inspection (clicking on the clickable parts of the papers, as well as pointing out applicants' weapons) also builds stress, so limit those actions to only when doing so is necessary to turn them away.
Therefore, the weapon confiscation routine is generally very stressful for applicants, especially those with concealed weapons that needs to be stripped (looking at you, noblewoman). Try to remember exactly which layer of clothes need to go for the weapon to become visible should make the process easier.