Cord is probably ineffective as a ball-stretching aid. You need something that is stiff, or at least semi-rigid, i.e. steel rings, weights, or stiff leather.
Stretching also takes considerable time - months... before any effect will be noticeable.
The safest method of starting a stretching regimine is probably via the use of stiff leather stretchers. These come with strap or buckle closures, so their diameter is adjustable/adaptable. The strap's widths generally range from 1/4" to as much as 4". Many of these will also have a spreader strap with a D-ring on the lower portion to allow easy attachment of weights to augment the effect.
Without exception, every company (and there are many) I've ever purchases from have delivered their product in simple non-descript cardbox boxes, no marking on the outside, and discreet shipping labels.