The simplest answer would be "a large pair of calipers". In fact, they make such a tool for exactly this task. See http://www.seritex.com/gpm-large-spreading-caliper-rounded-ends-108/
The GPM Large Spreading Caliper with rounded ends provides accurate
measurement of the distance between two points, where one or both
points may not be on a flat surface. This Large Spreading Caliper can
also be used for the measurement of Anterior-Posterior chest depth.
The ends of the spreading branches are rounded for the patient's
comfort, as opposed to the GPM Large Spreading Caliper model 109,
which has pointed ends.
The GPM Large Spreading Caliper with rounded ends is manufactured from
chrome plated steel. Hinged at the base, the two curved branches with
rounded ends are connected by a pivotal ruler, which is engraved in
millimeter intervals from 0 to 60 cm. The branches can be immobilized
in any position by a screw located on the slider which guides the
ruler. The ruler gives the precise distance between the two points
over which the measurement has been taken.
Or you could improvise by using something like this:
NOTE: The OP changed the question to include the "mobile and wearable" requirements, after this answer was written.