Can I skip the reporting of non significant results of a test? I mean report the means and SD, say it's not significant, but skip the test result and exact p.
One of the things which makes subsequent synthesis of primary studies and their meta-analysis difficult is when the authors of the primary studies just say "not significant". If you are convinced that you have presented enough information for synthesisers to reconstruct your analysis or if you believe your study is so poor that nobody will ever want to include it in their meta-analysis (just joking there) then publish in that format. If in doubt, please, please publish the details to make subsequent scientists life easier.
It is always best to present the results of significance testing, with confidence intervals as well as p.values. This aids researchers in meta-analyses, as well as gives clarification of what you consider to be significant/non-significant. Was the result marginally non-significant? We will never know if you don't tell us.
Presumably you will have already performed the tests, so if it is for saving space or not getting bogged down in tedious tables in your paper, remember that many journals accept use of online supplementary appendices. This can save space and headaches for curious readers.
Hope that helps :)