Easiest fix for this is to simply replace the velcro with something better. I wrote up a thing in another thread on an idea to use magnets to affix the strap to the mouse, which would be one way to do it. An alternative would be to pick up the tools to simply add an old-fashioned snap fastener to the mouse body and strap, so that it literally snaps onto the mouse.
Personally, I find the strap to be more of a pain than it's worth, since i have to move my hand between mouse and keyboard too frequently for it to be convenient, and relying on that instead of having a proper place to just grip the mouse with my thumb opposite of my hand was stupid. So, I simply adjusted the thumb joystick to where I could still use it when I needed to, but it wasn't in the way, took one of the replacement joystic caps, found a good place on the housing for the joystick where my thumb would rest naturally and give me a good pincer grip on the mouse like any other vertical mouse, and then filed a flat spot and glued the cap on. Problem solved.
As far as the strap itself, if i ever end up needing something that the strap would be useful for, instead of using the strap and affixing it, I'm just going to use some Kydex thermo-set plastic to make a back plate that comes up over my hand more, can be adjusted angle-wise, and then shape it so that it serves the purpose of the strap but without being so clingy/tight that I can't get my hand on and off of the mouse easily. Add some leather/neoprene padding to prevent the plastic from abrading my skin, and done. Total time to do it, from prototyping to final piece installation should probably take me an hour.