||Well, there's converting, and there's converting.
The best way is to use a tool that supports the NADCON method or software and convert the coordinates to NAD83. At that point, you might also use NADCON (but called the HARN method in ESRI software) to convert from NAD83 to NAD83 HARN, aka HPGN. There are some transformations that convert from NAD83/NAD83HARN to WGS84, but at least for the lower 48, the differences are under a meter, so the data accuracy may not warrant it.
NGS (http://www.ngs.noaa.gov) publishes both NADCON and CORPSCON programs. Both have file-based capabilities, but the file formats are bit convoluted. NADCON and HARN need supporting binary files to calculate the shifts.
There are simpler transformations that go directly from NAD27 to WGS84, but they aren't as accurate. They are also area of use based. In ESRI software, there are 25.
If you have 3.x, you could convert the coordinates to a shapefile, use the Projection Utility (it supports NADCON/HARN), and then add the new XY values to the new shapefile and export them.
ESRI Product Specialist