I don't wish to complicate your cycling at the moment, but it may be worth while to look into getting live plants at some point in the future. They would certainly benefit from the nitrate, as would the fish since the plants would be absorbing it. During the tricky process you're currently involved in, it would not be prudent to go digging around placing plants and disrupting the tank, but keep it in mind for post-cycle tank planning. Your other option for handling the nitrate would be to simply carry out more water changes than the typical fishkeeper would.
In a 38 gallon tank, four tetras (dependent upon the type, I suppose) would be a rather small population. I would suggest purchasing at least two more (tetras tend to be social fish) AFTER the cycle is completed. This will make your tank more interesting, as well as please your social fish. I say all of this assuming you have a small-sized variety of tetra. Remember that more fish will produce more ammonia. It will require a mini cycle to account for the increased bio-load.
As a side note, if you do decide to get plants or more fish, I would suggest quarantining them to prevent damaging your newly cycled tank. Typically, a 2-4 week quarantine is sufficient.
All of the above may be too much to think about now, but if you are a very serious hobbyist, it is worth considering.