Do not is present simple and in narrative sentences is supposed to mean a constant and regular action or some mental process or state to which continuous tense is not applied. It is kind of out of place in this context. Please refer, say, to Wiki for more information or just google "present simple vs present continuous".
Now about the rest of options.
If you have already decided you do not want to show "this" in the report and want to underline this is your plan you are going to follow, you can say:
[..] we are not showing this in the report.
Or, if you are not quite sure yet but are inclined not to show:
[..] we are not going to show this in the report.
Will not has a slight emphasis that the solution has just been done by you. You decide not to show this and immediately say:
[...] we will not show [...]
however, it also mean just the mere fact we will not show this in the report. Refer to this article about differences between be doing, be going to do and will do.
As for need not and should not, you correctly described their meaning, which one to use is up to you and depends on what you want to say.
PS For further reading, you may want to learn more about the phrase to be going to, modal verbs like should, owe, must etc, as well as aspects of present continuous use with regard to the future actions.