Publishing a paper with questionable statistics
Well, if you're having second thoughts is because deep down you have a solid reason for it.
And, you do, as you said in your text, the statistical data is lacking additional background support. If possible add more data to the existing data, and make changes to the text accordingly.
Is frequently found on research papers, some shortcuts when presenting experimental data that is lacking some explanation/support. For instance, changing the axis scales, present data in a normalized axis scale, among many others. These data presentation techniques will force the reviewers to spend more time analyzing your data looking for clues on lack of validity. In such cases, even if it gets published, later on, it will be reflected on the number of citations (for instance). To simply put, I don't recommend doing it nowadays.