Amazon doesn't make it possible to prevent a shipper from being chosen to fulfill a package, but you can request what they call "carrier deprioritization" via their customer support helpdesk, which will artificially weight the carrier in question so that their algorithm will opt against it unless it is the only carrier able to fulfill a given order.

I've had good success with this last year, after Amazon's own in-house fulfillment service caused me a series of issues due to erroneously failed deliveries; since I made that request, I haven't had a single shipment fulfilled via AMZL_US save those for which I requested same-day delivery of items present in the Canton warehouse. Other sorts of orders which AMZL_US would previously fulfill are instead now handled by UPS or FedEx.

If you have trouble with LaserShip, as I gather many do, you could probably do worse than to request Amazon deprioritize that carrier. If my experience is any guide, you may have to bounce from rep to rep a couple of times before you find someone who knows what you're talking about, but it's worth persisting, because the results are, at least in my experience, much worth the effort. Hope this helps!