I hope you aren't going to use a 5gal bucket to "store" your 1-2lbs of minnows in
... well, not unless you plan on changing their water every day. The cool/oxygenated water that your pumping device will provide, will probably be enough to keep them alive, temporarily ... but, their waste deposits will foul the water up, real quick ... and they'll start to die off. You might be better off with a 25gal (or larger) "tank" ... and using the suction cups to hold the pump onto the sides, and making a L joint in the T bar sprayer (so the spray bar will be out of the water).
I had one of those same pumps in my last boat ... I used it as an aerator. It was a strong circulator of water, and the spray pressure was strong enough to nearly beat minnows/shad/fish to death, in the shallow water of my livewell. I see by your picture, that it looks as though the extra height the water travels, is enough to diminish that force somewhat. I don't know what effect another couple of feet of height, of your T bar, would have on the spray/flow of water. That's why I suggested attaching the pump to the side of the larger tank, and use a pvc elbow to bring the T bar above the surface (of the deeper water level). You might get away with transporting a pound or two of minnows, in a 5gal bucket, with an air pump attached ... but, I wouldn't want to transport them far, or for very long. Nor would I want to try and keep them in one, for very long, either.
It may be just me, but IMHO ... 4gal of water just doesn't seem enough for several hundred minnows.
Have you thought about how you're going to "refrigerate" them, during the warmer days of the year ?? ... cp