The Elastic Wristband Lanyard from Official Sports ($2.95, here) is a simple device for carrying your whistle on your wrist. This allows you to let go of the whistle while you record game information, have a friendly conversation with a player, etc, while still keeping it quickly accessible.
The basic information given on the OSI website leaves out some important information. For starters, the wristband is not adjustable, per se. It is made of stretchy elastic material that should stretch to accommodate all but the largest of wrist sizes. An important note: if you have small wrist, e.g., you are a female referee or a young teenager, you may find this wristband is actually too large to feel secure.
The inside of the wristband features a soft nylon material that makes it quite comfortable. The plastic clip feels secure when new, but I wonder how it would hold up to repeated removal/replacement of the whistle.
The length of the lanyard itself is just right in my large hand, with a whistle attached. The lanyard itself measures 10.5 cm from the wristband to the end of the clip. The wristband is 9.5 cm wide when laid flat, with a circumference of about 7 cm (it obviously stretches to a larger size when worn). The stitching attaching the lanyard to the wristband seems secure enough.
In summary, if you prefer a wrist lanyard, you may want to try the OSI Elastic Wristband Lanyard. Without any moving parts to loosen, it should be very secure on your wrist, and, depending on your preference, you may find it a more comfortable alternative to traditional wrist lanyards.