If you do a quick search for 'bungee and wrist' you will find some different and interesting ideas.
I use the smallest bungee I could find {I think it's 3/16}. For my computer {Suunto Vyper}, I removed the wrist strap and slid the bungee under the strap pins, checked the fit for my wrist and tied the ends up and secured the ends. For my compass, I got myself a generic wrist mount, trimmed the straps off, drilled a couple of holes for the bungee and then secured the bungee. Your computer maybe different and it'll take a little fidgeting to get a good fit and the ends knotted and secure.
Here are a couple of quick pictures, the compass bungee is setup for adjustment between a drysuit and wetsuit, I simply undo one knot and it fits the drysuit. The computer bungee is in a state of experiment with a different loop ~ just playing.
Hope this helps.