I hate with a passion "picking" the hulls out of the action. I tuck the stock under my right arm, hit the lever with the fat part of my thumb, while holding the forearm with left hand...gun breaks open and I catch the empty hulls about 6-8" out of the gun, drop them in the hull bag, grab two loaded shells and in they go. In the hundreds of thousands of times I've done it, I'm pretty sure I can count on both hands the number of hulls I've dropped. Everybody does it different.
Being LH, I do the same in a mirror image version.
If that proves too difficult, all one has to do is turn the gun somewhat sideways and open the gun close to your vest so they pop out, hit your vest in the stomach, and then you can place them in your vest or trash