The Lapua brass with the small flash holes is probably also for small rifle primers, I wouldn't recommend reaming them out.
Universal depriming dies are cheap, available for both small and large primers (with the correct corresponding pins) and as the name suggests can be used for many different cartridges.
I'm not sure about Hornady, but on my Redding dies you can just swap in the smaller diameter pin. If you absolutely have to load today, swapping the pin is probably a better option than trying to drill out the flash holes.
BTW if you have "new Lapua brass" you don't need to deprime today, just run them through the sizing die to make sure the case mouths are round. So for now, just remove the pin temporarily and use it without a pin.