Odds are nothing will happen, not this time, not the next five or ten times. As much as I hate to say it, even the most routine preps we do are for very isolated incidents. You know how many times I've used my first aid gear in the last five years, once. I had a friend accidentally stab herself in the leg. Even that only required gauze and tape and a trip to the ER. Let alone more exotic preparations like CBRN events, which you would have to be extraordinarily unlucky to face in your entire life. Part of the reason that survival prep isn't very common, is that survival situations that break down the normal order of our lives aren't very common.

If I was this businessman, I'd have my normal pocket debris and appropriate clothing on me, and I'd have my waist pack kit, contingency clothing in my luggage, and all my clothes in my bag would be in large ziplock bags to make them, water, bug and dirt resistant. Odds are no-one would notice, but if it was a serious issue of embarrassment, the contents of my waist pack kit can easily be transferred to an extra shaving kit.

Side note, for business travel, shaving kits are the equivalent of camping stuff sacks. Put your survival kit in one, your laptop cables and bits in another. Anything small that needs to be organized can go in a different kit. A little colored cord can identify which is which.