I think the Olight Mini needs a rail to attach, which the Shield doesn't have.
I have an Olight Pro on my full size, great light for the money
One choice for the Shield are the Streamlight TRL-6, made for the 9mm and .40 Shield.
It's possible to modify the TRL-6 to fit the .45 Shield.
Other choice is the Lasermax with grip sense.
It can be had with red laser, or for more money, a green laser. And models to fit all 3 calibers of the Shield.
The grip sense is nice but very sensitive. If your second finger barely touches the bottom of the trigger guard the unit will turn on.
I keep the grip sense deactivated most of the time and just turn on with the button on either side ( same as the TRL-6 ).
Both lights are 100 lumen, the Lasermax having a "mint green" tinge to it.
Green is the easiest spectrum for our eyes to see, so it isn't so harsh when you turn it on in a dark environment.
I've had several TRL-6s and they are good, but I'd recommend spending the extra $70 and get the green laser Lasermax.
That green laser shows up well in the daylight too.
And the Lasermax is a more compact unit too.