You could drill holes around the lateral surface of something round and easy to carry, like a hockey puck, as a quick gauge. For example, a 1/4" SHCS has a maximum head diameter of 0.375. A letter size larger drill would be a "V" at 0.377 and allow for a little leeway yet still not fit the head of the next smaller or larger sized screws. Some trial and error may be needed. The hole could be marked on the face of the puck with the wrench size. In this case it is 3/16.

Here is a chart of US customary dimensions.

Another style could have holes drilled around the lateral edge with short pieces of each size hex wrench pressed into the holes and labeled by size. This would work better for recessed screws. Metric versions of each could be done in the same way.