I believe your linked light fixture is too intense for what you are planning. T5 tubes emit considerably stronger (more intense) light than regular T8 or T12 tubes. As you do not want CO2, and I agree with Angel this is unnecessary in the majority of well-planted aquaria, you do not want intense light.
The old "rule" of 1 watt per gallon of full spectrum really does work in most situations. This refers to regular (T8, T12) fluorescents, not T5 which as I mentioned are considerably more intense. Two T5 tubes approximately equal three regular. The fixtures are not interchangeable, just so you know.
The other consideration in this is the fish. Those you've mentioned come from dimly-lit dark waters in the forest. They will be less stressed and therefore healthier with less light; they will show better colouration under less light and with a dark substrate. Plants also look better with a dark substrate.
The photo below is of my former 33g which had one 25w Life-Glo 2 tube over it. The main plant is Anubias, and there are crypts along the front and floating Ceratopteris (water sprite). South American forest fish as you've mentioned. I don't have photos of this tank when it had Amazon swords, but they thrived. And the fish sparkled under less light.
With the dual-tube T5 you would have approximately six times more light than what is shown in these photos. That is simply way too much. The plants can't use all that, since CO2 from the fish won't balance, so algae will take over. Even with two regular or one T5 over this size of tank (36 inches, 33g) you will have double the light that I have in the photos. That's a lot of light.
My recommendation would be one regular tube fixture, with a Life-Glo tube. The photo is a Life-Glo 2 which is a tad less bright, so the Life-Glo would be a bit more, but sufficient for the plants and fish you've mentioned.