Hey Lawrence, how are you?
I would say that there is a difference between the two sentences you provided. Firstly, the first sentence should be rewritten as ''I did not (didn't) choose to use it'', as the form ''do not choose to...'' sounds a little awkward. In second place, it conveys the idea that it was not you who chose to use it, thus suggesting that someone else may have done it for you. As opposed to the first sentence, the second one ''I choose not to use it'' sounds good to my ears, and it is the one that best gives off the idea which you may be trying to imply here: you indeed make a choice (at the moment of speaking) or made a choice (at some time earlier in the past) and then you say: ''I choose not to use it'' (in the present tense) or ''I chose not to use it (in the past tense). Be that as it may, the very choice you make/made is/was NOT TO USE IT.
Did you get the idea?
Hope that helps!!! :)
Should you have any further questions, do not hesitate to contact me. I shall be pleased to help.