I'm sure you've heard it once, and a thousand times. Thumb breaks aren't recommended for concealed carry. Your weapon is already covered by one or more garments, you're adding another obstacle to retrieving your weapon.
Custom holster makers, be it kydex, leather or other, make their holsters to retain the weapon without such devices. Get into generic fitting holsters (size 1, 2, 3, etc.), then the strap may be necessary, because the holster isn't made for said gun.
That being said, Tim Start at
highdesertleather.com has been doing off-duty rigs for years and most of the departments he has dealt with require straps. He's good at it.
Nate