Niamey in Niger is now on the equator, I think the northern tip of Australia is too, Ecuador is now very slightly south of it, and so forth. You can visualise this to some extent as a sine wave plotted on a normal map of the Earth, with the peaks 15 degrees North of the current equator at the Greenwich Meridian, 15 degrees south at 180 degrees.
The snag is that what I will need is a map of the earth plotted with the new equator as a straight line, and the land masses shifted accordingly. I can probably fake this to some extent by distorting a normal map, but all map projections lie to some extent about the position and size of land masses near the poles, and changing their position without changing the relative sizes will make this worse. I'm not enough of a geographer to get this right. If anyone has software or the skills to do this properly, or can think of a better way to do it, I'd love to hear from you.
I'm not too sure what to do about the degree of axial tilt. 20 degrees or so seems to work well for having seasons and forming nice big ice caps, but would anyone stupid enough to do this in the first place think of that?