Im going with not possible. The p-value can be no better than knowing the actual ranks of the data, and the ratio is no better than knowing the actual means. The term 'better' means ranks of data implies p-value, and knowledge of the means implies a ratio, obviously. But even knowing the ranks and means, it is pretty clear, in my reckoning that you can conjure up any sd's you be wantin'. Conclusion: get the original data, or move on...