While 250+ fields is an ugly database design, the error message is actually based on the 4000 byte record width limitation of dBase, which can be reached in as few as sixteen 254-character string fields. The dBase III specification also has a 100 field limit, which ArcGIS ignores, but it does honor the hard limit of 255 fields (field count is a single byte in the dBase header).
File geodatabase does not have the 4K buffer limitation, and supports 64K columns (which is far greater than the database limitations of 256 or 512, depending on ArcGIS version).
So your options are to slice the the table width to something that dBase can support or to use a format other than shapefile.
- V